A294582 - OEIS

A294582

Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} 1/(1 - j^k*x^j)^j.

1, 1, 1, 1, 1, 3, 1, 1, 5, 6, 1, 1, 9, 14, 13, 1, 1, 17, 36, 42, 24, 1, 1, 33, 98, 148, 103, 48, 1, 1, 65, 276, 546, 489, 289, 86, 1, 1, 129, 794, 2068, 2467, 1959, 690, 160, 1, 1, 257, 2316, 7962, 12969, 14281, 6326, 1771, 282, 1, 1, 513, 6818, 30988, 70243

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OFFSET

0,6

LINKS

Seiichi Manyama, Antidiagonals n = 0..139, flattened

FORMULA

A(0,k) = 1 and A(n,k) = (1/n) * Sum_{j=1..n} (Sum_{d|j} d^(2+k*j/d)) * A(n-j,k) for n > 0.

EXAMPLE

Square array begins:

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

3, 5, 9, 17, 33, ...

6, 14, 36, 98, 276, ...