A368487 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} k^j * binomial(j+k-1,j).
1, 1, 1, 1, 2, 1, 1, 5, 3, 1, 1, 10, 17, 4, 1, 1, 17, 64, 49, 5, 1, 1, 26, 177, 334, 129, 6, 1, 1, 37, 401, 1457, 1549, 321, 7, 1, 1, 50, 793, 4776, 10417, 6652, 769, 8, 1, 1, 65, 1422, 12889, 48526, 67761, 27064, 1793, 9, 1, 1, 82, 2369, 30234, 176185, 442276, 411825, 105796, 4097, 10, 1
Offset: 0
Examples
Square array begins: 1, 1, 1, 1, 1, 1, ... 1, 2, 5, 10, 17, 26, ... 1, 3, 17, 64, 177, 401, ... 1, 4, 49, 334, 1457, 4776, ... 1, 5, 129, 1549, 10417, 48526, ... 1, 6, 321, 6652, 67761, 442276, ...
Crossrefs
Programs
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PARI
T(n, k) = sum(j=0, n, k^j*binomial(j+k-1, j));
Formula
G.f. of column k: 1/((1-x) * (1-k*x)^k).