OFFSET
0,12
COMMENTS
Column k is the diagonal of the rational function 1 / (Product_{j=1..k} (1-x_j) + k * Product_{j=1..k} x_j) for k>0.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 0, -1, -2, -3, -4, ...
1, 0, -3, -14, -47, -134, ...
1, 0, 11, 136, 909, 4736, ...
1, 0, 1, 106, 3585, 61906, ...
1, 0, -81, -8492, -323523, -8065624, ...
MATHEMATICA
T[n_, k_] := Sum[If[k == j == 0, 1, (-k)^j] * Binomial[n, j]^k, {j, 0, n}]; Table[T[k, n-k], {n, 0, 10}, {k, 0, n}] // Flatten (* Amiram Eldar, May 01 2021 *)
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Jul 11 2020
STATUS
approved