A358050 - OEIS

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A358050

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

1, 1, 0, 1, 2, 0, 1, 4, 3, 0, 1, 6, 16, 4, 0, 1, 8, 39, 64, 5, 0, 1, 10, 72, 258, 256, 6, 0, 1, 12, 115, 664, 1719, 1024, 7, 0, 1, 14, 168, 1360, 6184, 11496, 4096, 8, 0, 1, 16, 231, 2424, 16265, 57888, 77052, 16384, 9, 0, 1, 18, 304, 3934, 35400, 195660, 543544, 517194, 65536, 10, 0

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,5

LINKS

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

FORMULA

T(n,k) = Sum_{j=0..n} (k-1)^(n-j) * binomial(k*n+1,j).

T(n,k) = Sum_{j=0..n} k^(n-j) * binomial((k-1)*n+j,j).

EXAMPLE

Square array begins:

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

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