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A294758 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*j)*x^j) in powers of x. 3
1, 1, 1, 1, 1, 2, 1, 1, 5, 3, 1, 1, 17, 32, 5, 1, 1, 65, 746, 304, 7, 1, 1, 257, 19748, 66538, 3537, 11, 1, 1, 1025, 531698, 16801060, 9843827, 52010, 15, 1, 1, 4097, 14349932, 4295564530, 30535638897, 2188210276, 895397, 22, 1, 1, 16385, 387424586, 1099527026284, 95371863254051, 101591953731770, 680615495493, 18016416, 30 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Seiichi Manyama, Antidiagonals n = 0..52, flattened

FORMULA

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

EXAMPLE

Square array begins:

   1,   1,     1,        1, ...

   1,   1,     1,        1, ...

   2,   5,    17,       65, ...

   3,  32,   746,    19748, ...

   5, 304, 66538, 16801060, ...

CROSSREFS

Columns k=0..1 give A000041, A023882.

Rows n=0-1 give A000012.

Cf. A294653.

Sequence in context: A125860 A294585 A283674 * A125800 A264698 A263296

Adjacent sequences:  A294755 A294756 A294757 * A294759 A294760 A294761

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, Nov 08 2017

STATUS

approved

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Last modified February 24 18:55 EST 2021. Contains 341584 sequences. (Running on oeis4.)