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.

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

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