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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. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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, ...

    1,  1,   1,   1,    1, ...

    3,  5,   9,  17,   33, ...

    6, 14,  36,  98,  276, ...

   13, 42, 148, 546, 2068, ...

CROSSREFS

Columns k=0..2 give A000219, A266941, A285674.

Rows n=0-1 give A000012.

Cf. A292193, A294580.

Sequence in context: A114172 A271942 A121522 * A294589 A204027 A080842

Adjacent sequences:  A294579 A294580 A294581 * A294583 A294584 A294585

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, Nov 02 2017

STATUS

approved

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Last modified February 29 05:25 EST 2020. Contains 332353 sequences. (Running on oeis4.)