A062534 Table by antidiagonals of coefficient of x^k in expansion of 1/((1+x)^2*(1-x)^n).

1, -2, 1, 3, -1, 1, -4, 2, 0, 1, 5, -2, 2, 1, 1, -6, 3, 0, 3, 2, 1, 7, -3, 3, 3, 5, 3, 1, -8, 4, 0, 6, 8, 8, 4, 1, 9, -4, 4, 6, 14, 16, 12, 5, 1, -10, 5, 0, 10, 20, 30, 28, 17, 6, 1, 11, -5, 5, 10, 30, 50, 58, 45, 23, 7, 1, -12, 6, 0, 15, 40, 80, 108, 103, 68, 30, 8, 1, 13, -6, 6, 15, 55, 120, 188, 211, 171, 98, 38, 9, 1, -14, 7, 0, 21, 70, 175

Offset: 0

Author

Henry Bottomley, Jun 25 2001

Keywords

• sign
• tabl

Crossrefs

Rows are effectively (with minor adjustments): A038608, A001057, A027656, A008805, A006918, A002624, A028346. Cf. A058394 which (adjusting for signs and an overlap of three rows) is effectively the continuation of this table for negative n.

Formula

Each row is partial sum of preceding row, i.e. T(n, k)=T(n-1, k)+T(n, k-1) with T(0, k)=(k+1)*(-1)^k and T(n, 0)=1.