A366986 - OEIS

A366986

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

1, 1, 2, 1, 3, 2, 1, 4, 4, 3, 1, 5, 7, 7, 2, 1, 6, 11, 14, 6, 4, 1, 7, 16, 25, 16, 12, 2, 1, 8, 22, 41, 36, 31, 8, 4, 1, 9, 29, 63, 71, 71, 29, 15, 3, 1, 10, 37, 92, 127, 147, 85, 50, 13, 4, 1, 11, 46, 129, 211, 280, 211, 145, 52, 18, 2, 1, 12, 56, 175, 331, 498, 463, 371, 176, 74, 12, 6

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..78.

FORMULA

G.f. of column k: Sum_{j>=1} x^j/(1 - x^j)^(k+1).

EXAMPLE

Square array begins:

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

2, 3, 4, 5, 6, 7, 8, ...

2, 4, 7, 11, 16, 22, 29, ...