Triangle A231599: T(n, k) is the coefficient of xk in (1-x)·(1-x2)·...·(1-xn)
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(0, 0)
1
(1, 0)
1
(1, 1)
-1
(2, 0)
1
(2, 1)
-1
(2, 2)
-1
(2, 3)
1
(3, 0)
1
(3, 1)
-1
(3, 2)
-1
(3, 3)
0
(3, 4)
1
(3, 5)
1
(3, 6)
-1
(4, 0)
1
(4, 1)
-1
(4, 2)
-1
(4, 3)
0
(4, 4)
0
(4, 5)
2
(4, 6)
0
(4, 7)
0
(4, 8)
-1
(4, 9)
-1
(4, 10)
1
(5, 0)
1
(5, 1)
-1
(5, 2)
-1
(5, 3)
0
(5, 4)
0
(5, 5)
1
(5, 6)
1
(5, 7)
1
(5, 8)
-1
(5, 9)
-1
(5, 10)
-1
(5, 11)
0
(5, 12)
0
(5, 13)
1
(5, 14)
1
(5, 15)
-1
(6, 0)
1
(6, 1)
-1
(6, 2)
-1
(6, 3)
0
(6, 4)
0
(6, 5)
1
(6, 6)
0
(6, 7)
2
(6, 8)
0
(6, 9)
-1
(6, 10)
-1
(6, 11)
-1
(6, 12)
-1
(6, 13)
0
(6, 14)
2
(6, 15)
0
(6, 16)
1
(6, 17)
0
(6, 18)
0
(6, 19)
-1
(6, 20)
-1
(6, 21)
1
(7, 0)
1
(7, 1)
-1
(7, 2)
-1
(7, 3)
0
(7, 4)
0
(7, 5)
1
(7, 6)
0
(7, 7)
1
(7, 8)
1
(7, 9)
0
(7, 10)
-1
(7, 11)
-1
(7, 12)
-2
(7, 13)
0
(7, 14)
0
(7, 15)
0
(7, 16)
2
(7, 17)
1
(7, 18)
1
(7, 19)
0
(7, 20)
-1
(7, 21)
-1
(7, 22)
0
(7, 23)
-1
(7, 24)
0
(7, 25)
0
(7, 26)
1
(7, 27)
1
(7, 28)
-1
(8, 0)
1
(8, 1)
-1
(8, 2)
-1
(8, 3)
0
(8, 4)
0
(8, 5)
1
(8, 6)
0
(8, 7)
1
(8, 8)
0
(8, 9)
1
(8, 10)
0
(8, 11)
-1
(8, 12)
-2
(8, 13)
-1
(8, 14)
0
(8, 15)
-1
(8, 16)
1
(8, 17)
1
(8, 18)
2
(8, 19)
1
(8, 20)
1
(8, 21)
-1
(8, 22)
0
(8, 23)
-1
(8, 24)
-2
(8, 25)
-1
(8, 26)
0
(8, 27)
1
(8, 28)
0
(8, 29)
1
(8, 30)
0
(8, 31)
1
(8, 32)
0
(8, 33)
0
(8, 34)
-1
(8, 35)
-1
(8, 36)
1
(9, 0)
1
(9, 1)
-1
(9, 2)
-1
(9, 3)
0
(9, 4)
0
(9, 5)
1
(9, 6)
0
(9, 7)
1
(9, 8)
0
(9, 9)
0
(9, 10)
1
(9, 11)
0
(9, 12)
-2
(9, 13)
-1
(9, 14)
-1
(9, 15)
-1
(9, 16)
0
(9, 17)
1
(9, 18)
1
(9, 19)
1
(9, 20)
2
(9, 21)
1
(9, 22)
1
(9, 23)
-1
(9, 24)
-1
(9, 25)
-2
(9, 26)
-1
(9, 27)
-1
(9, 28)
-1
(9, 29)
0
(9, 30)
1
(9, 31)
1
(9, 32)
1
(9, 33)
2
(9, 34)
0
(9, 35)
-1
(9, 36)
0
(9, 37)
0
(9, 38)
-1
(9, 39)
0
(9, 40)
-1
(9, 41)
0
(9, 42)
0
(9, 43)
1
(9, 44)
1
(9, 45)
-1
(10, 0)
1
(10, 1)
-1
(10, 2)
-1
(10, 3)
0
(10, 4)
0
(10, 5)
1
(10, 6)
0
(10, 7)
1
(10, 8)
0
(10, 9)
0
(10, 10)
0
(10, 11)
1
(10, 12)
-1
(10, 13)
-1
(10, 14)
-1
(10, 15)
-2
(10, 16)
0
(10, 17)
0
(10, 18)
1
(10, 19)
1
(10, 20)
1
(10, 21)
1
(10, 22)
3
(10, 23)
0
(10, 24)
0
(10, 25)
-1
(10, 26)
-1
(10, 27)
-2
(10, 28)
-2
(10, 29)
-1
(10, 30)
-1
(10, 31)
0
(10, 32)
0
(10, 33)
3
(10, 34)
1
(10, 35)
1
(10, 36)
1
(10, 37)
1
(10, 38)
0
(10, 39)
0
(10, 40)
-2
(10, 41)
-1
(10, 42)
-1
(10, 43)
-1
(10, 44)
1
(10, 45)
0
(10, 46)
0
(10, 47)
0
(10, 48)
1
(10, 49)
0
(10, 50)
1
(10, 51)
0
(10, 52)
0
(10, 53)
-1
(10, 54)
-1
(10, 55)
1
(11, 0)
1
(11, 1)
-1
(11, 2)
-1
(11, 3)
0
(11, 4)
0
(11, 5)
1
(11, 6)
0
(11, 7)
1
(11, 8)
0
(11, 9)
0
(11, 10)
0
(11, 11)
0
(11, 12)
0
(11, 13)
0
(11, 14)
-1
(11, 15)
-2
(11, 16)
-1
(11, 17)
0
(11, 18)
0
(11, 19)
1
(11, 20)
1
(11, 21)
1
(11, 22)
2
(11, 23)
1
(11, 24)
1
(11, 25)
0
(11, 26)
1
(11, 27)
-2
(11, 28)
-2
(11, 29)
-2
(11, 30)
-2
(11, 31)
-1
(11, 32)
-1
(11, 33)
0
(11, 34)
1
(11, 35)
1
(11, 36)
2
(11, 37)
2
(11, 38)
2
(11, 39)
2
(11, 40)
-1
(11, 41)
0
(11, 42)
-1
(11, 43)
-1
(11, 44)
-2
(11, 45)
-1
(11, 46)
-1
(11, 47)
-1
(11, 48)
0
(11, 49)
0
(11, 50)
1
(11, 51)
2
(11, 52)
1
(11, 53)
0
(11, 54)
0
(11, 55)
0
(11, 56)
0
(11, 57)
0
(11, 58)
0
(11, 59)
-1
(11, 60)
0
(11, 61)
-1
(11, 62)
0
(11, 63)
0
(11, 64)
1
(11, 65)
1
(11, 66)
-1
(12, 0)
1
(12, 1)
-1
(12, 2)
-1
(12, 3)
0
(12, 4)
0
(12, 5)
1
(12, 6)
0
(12, 7)
1
(12, 8)
0
(12, 9)
0
(12, 10)
0
(12, 11)
0
(12, 12)
-1
(12, 13)
1
(12, 14)
0
(12, 15)
-2
(12, 16)
-1
(12, 17)
-1
(12, 18)
0
(12, 19)
0
(12, 20)
1
(12, 21)
1
(12, 22)
2
(12, 23)
1
(12, 24)
1
(12, 25)
0
(12, 26)
2
(12, 27)
0
(12, 28)
-1
(12, 29)
-2
(12, 30)
-2
(12, 31)
-2
(12, 32)
-2
(12, 33)
-1
(12, 34)
-1
(12, 35)
0
(12, 36)
1
(12, 37)
2
(12, 38)
1
(12, 39)
4
(12, 40)
1
(12, 41)
2
(12, 42)
1
(12, 43)
0
(12, 44)
-1
(12, 45)
-1
(12, 46)
-2
(12, 47)
-2
(12, 48)
-2
(12, 49)
-2
(12, 50)
-1
(12, 51)
0
(12, 52)
2
(12, 53)
0
(12, 54)
1
(12, 55)
1
(12, 56)
2
(12, 57)
1
(12, 58)
1
(12, 59)
0
(12, 60)
0
(12, 61)
-1
(12, 62)
-1
(12, 63)
-2
(12, 64)
0
(12, 65)
1
(12, 66)
-1
(12, 67)
0
(12, 68)
0
(12, 69)
0
(12, 70)
0
(12, 71)
1
(12, 72)
0
(12, 73)
1
(12, 74)
0
(12, 75)
0
(12, 76)
-1
(12, 77)
-1
(12, 78)
1
(13, 0)
1
(13, 1)
-1
(13, 2)
-1
(13, 3)
0
(13, 4)
0
(13, 5)
1
(13, 6)
0
(13, 7)
1
(13, 8)
0
(13, 9)
0
(13, 10)
0
(13, 11)
0
(13, 12)
-1
(13, 13)
0
(13, 14)
1
(13, 15)
-1
(13, 16)
-1
(13, 17)
-1
(13, 18)
-1
(13, 19)
0
(13, 20)
0
(13, 21)
1
(13, 22)
2
(13, 23)
1
(13, 24)
1
(13, 25)
1
(13, 26)
1
(13, 27)
0
(13, 28)
1
(13, 29)
-1
(13, 30)
-1
(13, 31)
-2
(13, 32)
-2
(13, 33)
-2
(13, 34)
-2
(13, 35)
-2
(13, 36)
0
(13, 37)
1
(13, 38)
1
(13, 39)
2
(13, 40)
1
(13, 41)
3
(13, 42)
3
(13, 43)
2
(13, 44)
1
(13, 45)
1
(13, 46)
-1
(13, 47)
-1
(13, 48)
-2
(13, 49)
-3
(13, 50)
-3
(13, 51)
-1
(13, 52)
-2
(13, 53)
-1
(13, 54)
-1
(13, 55)
0
(13, 56)
2
(13, 57)
2
(13, 58)
2
(13, 59)
2
(13, 60)
2
(13, 61)
1
(13, 62)
1
(13, 63)
-1
(13, 64)
0
(13, 65)
-1
(13, 66)
-1
(13, 67)
-1
(13, 68)
-1
(13, 69)
-2
(13, 70)
-1
(13, 71)
0
(13, 72)
0
(13, 73)
1
(13, 74)
1
(13, 75)
1
(13, 76)
1
(13, 77)
-1
(13, 78)
0
(13, 79)
1
(13, 80)
0
(13, 81)
0
(13, 82)
0
(13, 83)
0
(13, 84)
-1
(13, 85)
0
(13, 86)
-1
(13, 87)
0
(13, 88)
0
(13, 89)
1
(13, 90)
1
(13, 91)
-1
(14, 0)
1
(14, 1)
-1
(14, 2)
-1
(14, 3)
0
(14, 4)
0
(14, 5)
1
(14, 6)
0
(14, 7)
1
(14, 8)
0
(14, 9)
0
(14, 10)
0
(14, 11)
0
(14, 12)
-1
(14, 13)
0
(14, 14)
0
(14, 15)
0
(14, 16)
0
(14, 17)
-1
(14, 18)
-1
(14, 19)
-1
(14, 20)
0
(14, 21)
0
(14, 22)
2
(14, 23)
1
(14, 24)
1
(14, 25)
1
(14, 26)
2
(14, 27)
0
(14, 28)
0
(14, 29)
0
(14, 30)
0
(14, 31)
-1
(14, 32)
-1
(14, 33)
-2
(14, 34)
-2
(14, 35)
-3
(14, 36)
-2
(14, 37)
0
(14, 38)
0
(14, 39)
1
(14, 40)
0
(14, 41)
3
(14, 42)
2
(14, 43)
3
(14, 44)
2
(14, 45)
3
(14, 46)
1
(14, 47)
1
(14, 48)
0
(14, 49)
-1
(14, 50)
-3
(14, 51)
-2
(14, 52)
-3
(14, 53)
-3
(14, 54)
-2
(14, 55)
-3
(14, 56)
-1
(14, 57)
0
(14, 58)
1
(14, 59)
1
(14, 60)
3
(14, 61)
2
(14, 62)
3
(14, 63)
2
(14, 64)
3
(14, 65)
0
(14, 66)
1
(14, 67)
0
(14, 68)
0
(14, 69)
-2
(14, 70)
-3
(14, 71)
-2
(14, 72)
-2
(14, 73)
-1
(14, 74)
-1
(14, 75)
0
(14, 76)
0
(14, 77)
0
(14, 78)
0
(14, 79)
2
(14, 80)
1
(14, 81)
1
(14, 82)
1
(14, 83)
2
(14, 84)
0
(14, 85)
0
(14, 86)
-1
(14, 87)
-1
(14, 88)
-1
(14, 89)
0
(14, 90)
0
(14, 91)
0
(14, 92)
0
(14, 93)
-1
(14, 94)
0
(14, 95)
0
(14, 96)
0
(14, 97)
0
(14, 98)
1
(14, 99)
0
(14, 100)
1
(14, 101)
0
(14, 102)
0
(14, 103)
-1
(14, 104)
-1
(14, 105)
1
(15, 0)
1
(15, 1)
-1
(15, 2)
-1
(15, 3)
0
(15, 4)
0
(15, 5)
1
(15, 6)
0
(15, 7)
1
(15, 8)
0
(15, 9)
0
(15, 10)
0
(15, 11)
0
(15, 12)
-1
(15, 13)
0
(15, 14)
0
(15, 15)
-1
(15, 16)
1
(15, 17)
0
(15, 18)
-1
(15, 19)
-1
(15, 20)
-1
(15, 21)
0
(15, 22)
1
(15, 23)
1
(15, 24)
1
(15, 25)
1
(15, 26)
2
(15, 27)
1
(15, 28)
0
(15, 29)
0
(15, 30)
0
(15, 31)
-1
(15, 32)
0
(15, 33)
-1
(15, 34)
-1
(15, 35)
-3
(15, 36)
-2
(15, 37)
-2
(15, 38)
-1
(15, 39)
0
(15, 40)
-1
(15, 41)
1
(15, 42)
2
(15, 43)
3
(15, 44)
2
(15, 45)
3
(15, 46)
2
(15, 47)
2
(15, 48)
2
(15, 49)
1
(15, 50)
0
(15, 51)
0
(15, 52)
-3
(15, 53)
-3
(15, 54)
-3
(15, 55)
-3
(15, 56)
-4
(15, 57)
-2
(15, 58)
-2
(15, 59)
-1
(15, 60)
0
(15, 61)
1
(15, 62)
2
(15, 63)
2
(15, 64)
4
(15, 65)
3
(15, 66)
3
(15, 67)
3
(15, 68)
3
(15, 69)
0
(15, 70)
0
(15, 71)
-1
(15, 72)
-2
(15, 73)
-2
(15, 74)
-2
(15, 75)
-3
(15, 76)
-2
(15, 77)
-3
(15, 78)
-2
(15, 79)
-1
(15, 80)
1
(15, 81)
0
(15, 82)
1
(15, 83)
2
(15, 84)
2
(15, 85)
3
(15, 86)
1
(15, 87)
1
(15, 88)
0
(15, 89)
1
(15, 90)
0
(15, 91)
0
(15, 92)
0
(15, 93)
-1
(15, 94)
-2
(15, 95)
-1
(15, 96)
-1
(15, 97)
-1
(15, 98)
-1
(15, 99)
0
(15, 100)
1
(15, 101)
1
(15, 102)
1
(15, 103)
0
(15, 104)
-1
(15, 105)
1
(15, 106)
0
(15, 107)
0
(15, 108)
1
(15, 109)
0
(15, 110)
0
(15, 111)
0
(15, 112)
0
(15, 113)
-1
(15, 114)
0
(15, 115)
-1
(15, 116)
0
(15, 117)
0
(15, 118)
1
(15, 119)
1
(15, 120)
-1
(16, 0)
1
(16, 1)
-1
(16, 2)
-1
(16, 3)
0
(16, 4)
0
(16, 5)
1
(16, 6)
0
(16, 7)
1
(16, 8)
0
(16, 9)
0
(16, 10)
0
(16, 11)
0
(16, 12)
-1
(16, 13)
0
(16, 14)
0
(16, 15)
-1
(16, 16)
0
(16, 17)
1
(16, 18)
0
(16, 19)
-1
(16, 20)
-1
(16, 21)
-1
(16, 22)
1
(16, 23)
0
(16, 24)
1
(16, 25)
1
(16, 26)
2
(16, 27)
1
(16, 28)
1
(16, 29)
0
(16, 30)
0
(16, 31)
0
(16, 32)
-1
(16, 33)
-1
(16, 34)
0
(16, 35)
-2
(16, 36)
-1
(16, 37)
-2
(16, 38)
-2
(16, 39)
-1
(16, 40)
-2
(16, 41)
0
(16, 42)
0
(16, 43)
2
(16, 44)
2
(16, 45)
3
(16, 46)
2
(16, 47)
3
(16, 48)
2
(16, 49)
2
(16, 50)
1
(16, 51)
3
(16, 52)
-1
(16, 53)
-1
(16, 54)
-2
(16, 55)
-3
(16, 56)
-3
(16, 57)
-3
(16, 58)
-4
(16, 59)
-4
(16, 60)
-2
(16, 61)
-2
(16, 62)
0
(16, 63)
0
(16, 64)
2
(16, 65)
2
(16, 66)
3
(16, 67)
3
(16, 68)
6
(16, 69)
3
(16, 70)
3
(16, 71)
2
(16, 72)
2
(16, 73)
0
(16, 74)
0
(16, 75)
-2
(16, 76)
-2
(16, 77)
-4
(16, 78)
-4
(16, 79)
-3
(16, 80)
-3
(16, 81)
-3
(16, 82)
-2
(16, 83)
-1
(16, 84)
-1
(16, 85)
3
(16, 86)
1
(16, 87)
2
(16, 88)
2
(16, 89)
3
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