A350594 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) is Sum_{j=0..2*n} (-1)^(n+j) * binomial(2*n,j)^k.
1, 1, -1, 1, 0, 1, 1, 2, 0, -1, 1, 6, 6, 0, 1, 1, 14, 90, 20, 0, -1, 1, 30, 786, 1680, 70, 0, 1, 1, 62, 5730, 61340, 34650, 252, 0, -1, 1, 126, 38466, 1696800, 5562130, 756756, 924, 0, 1, 1, 254, 247170, 41312060, 613591650, 549676764, 17153136, 3432, 0, -1
Offset: 0
Examples
Square array begins: 1, 1, 1, 1, 1, 1, ... -1, 0, 2, 6, 14, 30, ... 1, 0, 6, 90, 786, 5730, ... -1, 0, 20, 1680, 61340, 1696800, ... 1, 0, 70, 34650, 5562130, 613591650, ... -1, 0, 252, 756756, 549676764, 248832363780, ...
Links
- Seiichi Manyama, Antidiagonals n = 0..50, flattened
Crossrefs
Programs
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PARI
T(n, k) = sum(j=0, 2*n, (-1)^(n+j)*binomial(2*n, j)^k);