OFFSET
0,10
COMMENTS
T(n,k) is the constant term in the expansion of (-2 + Product_{j=1..k-1} (1 + x_j) + Product_{j=1..k-1} (1 + 1/x_j))^n for k > 0.
LINKS
Seiichi Manyama, Antidiagonals n = 0..100, flattened
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 0, 0, 0, 0, 0, ...
-1, 0, 2, 6, 14, 30, ...
2, 0, 0, 12, 72, 300, ...
-3, 0, 6, 90, 882, 6690, ...
4, 0, 0, 360, 8400, 124920, ...
MATHEMATICA
T[n_, k_] := Sum[(-2)^(n-i) * Binomial[n, i] * Sum[Binomial[i, j]^k, {j, 0, i}], {i, 0, n}]; Table[T[k, n - k], {n, 0, 10}, {k, 0, n}] // Flatten (* Amiram Eldar, May 06 2021 *)
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Oct 27 2019
STATUS
approved