A061298 Table by antidiagonals of rows of sequences where each row is binomial transform of preceding row and row 1 is (1,2,1,2,1,2,1,2,...).

1, 1, 1, -2, 2, 1, 4, 1, 3, 1, -8, 2, 6, 4, 1, 16, 1, 12, 13, 5, 1, -32, 2, 24, 40, 22, 6, 1, 64, 1, 48, 121, 92, 33, 7, 1, -128, 2, 96, 364, 376, 174, 46, 8, 1, 256, 1, 192, 1093, 1520, 897, 292, 61, 9, 1, -512, 2, 384, 3280, 6112, 4566, 1816, 452, 78, 10, 1, 1024, 1, 768, 9841, 24512, 23073, 11152, 3289, 660, 97, 11, 1, -2048

Offset: 0

Author

Henry Bottomley, Jun 05 2001

Keywords

• sign
• tabl

Crossrefs

Rows include A011782 (but signed), A000034, A003945, A003462, A010036. Columns include A000012, A000027, A028872.

Formula

T(n, k) =(3n^k-(n-2)^k)/2. Coefficient of x^k in expansion of (1-(n-3)x)/((1-nx)(1-(n-2)x)).