A362079 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = [x^n] 1/(1 - x*(1+x)^n)^k.
1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 7, 10, 0, 1, 4, 12, 28, 45, 0, 1, 5, 18, 55, 145, 251, 0, 1, 6, 25, 92, 315, 896, 1624, 0, 1, 7, 33, 140, 571, 2106, 6328, 11908, 0, 1, 8, 42, 200, 930, 4076, 15946, 50212, 97545, 0, 1, 9, 52, 273, 1410, 7026, 32718, 134730, 441489, 880660, 0
Offset: 0
Examples
Square array begins: 1, 1, 1, 1, 1, 1, ... 0, 1, 2, 3, 4, 5, ... 0, 3, 7, 12, 18, 25, ... 0, 10, 28, 55, 92, 140, ... 0, 45, 145, 315, 571, 930, ... 0, 251, 896, 2106, 4076, 7026, ...
Crossrefs
Programs
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PARI
T(n, k) = sum(j=0, n, binomial(j+k-1, j)*binomial(n*j, n-j));
Formula
T(n,k) = Sum_{j=0..n} (-1)^j * binomial(-k,j) * binomial(n*j,n-j) = Sum_{j=0..n} binomial(j+k-1,j) * binomial(n*j,n-j).