A368506 - OEIS

A368506

Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} k^(n-j) * binomial(j+k-1,j).

1, 1, 0, 1, 2, 0, 1, 4, 3, 0, 1, 6, 11, 4, 0, 1, 8, 24, 26, 5, 0, 1, 10, 42, 82, 57, 6, 0, 1, 12, 65, 188, 261, 120, 7, 0, 1, 14, 93, 360, 787, 804, 247, 8, 0, 1, 16, 126, 614, 1870, 3204, 2440, 502, 9, 0, 1, 18, 164, 966, 3810, 9476, 12900, 7356, 1013, 10, 0

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OFFSET

0,5

LINKS

Table of n, a(n) for n=0..65.

FORMULA

G.f. of column k: 1/((1-k*x) * (1-x)^k).

EXAMPLE

Square array begins:

1, 1, 1, 1, 1, 1, 1, ...

0, 2, 4, 6, 8, 10, 12, ...

0, 3, 11, 24, 42, 65, 93, ...