A294585 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^k).

1, 1, 1, 1, 1, 2, 1, 1, 5, 3, 1, 1, 17, 14, 5, 1, 1, 65, 98, 42, 7, 1, 1, 257, 794, 514, 103, 11, 1, 1, 1025, 6818, 7194, 2435, 289, 15, 1, 1, 4097, 60074, 107170, 69475, 12752, 690, 22, 1, 1, 16385, 535538, 1649322, 2177411, 715277, 58849, 1771, 30

Offset

0,6

Links

Seiichi Manyama, Antidiagonals n = 0..113, flattened

Formula

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

Example

Square array begins:
   1,  1,   1,    1,      1, ...
   1,  1,   1,    1,      1, ...
   2,  5,  17,   65,    257, ...
   3, 14,  98,  794,   6818, ...
   5, 42, 514, 7194, 107170, ...

Crossrefs

Columns k=0..2 give A000041, A266941, A294586.

Rows n=0-1 give A000012.

Sequence in context: A308292 A117396 A125860 * A283674 A294758 A125800

Adjacent sequences: A294582 A294583 A294584 * A294586 A294587 A294588

Keyword

nonn,tabl

Author

Seiichi Manyama, Nov 03 2017

Status

approved