A294756 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)^j(k*j) in powers of x.

1, 1, 1, 1, 1, 2, 1, 1, 17, 3, 1, 1, 257, 746, 5, 1, 1, 4097, 531698, 66442, 7, 1, 1, 65537, 387424586, 4295533810, 9843731, 11, 1, 1, 1048577, 282429602018, 281475372654922, 95371863223331, 2187951485, 15, 1, 1, 16777217, 205891133143226, 18446744358295025890, 931322857677725493491, 4738477951108288824, 680615166718, 22

Offset

0,6

Links

Seiichi Manyama, Antidiagonals n = 0..38, flattened

Formula

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

Example

Square array begins:
   1,     1,          1,               1, ...
   1,     1,          1,               1, ...
   2,    17,        257,            4097, ...
   3,   746,     531698,       387424586, ...
   5, 66442, 4295533810, 281475372654922, ...

Crossrefs

Columns k=0..1 give A000041, A294757.

Rows n=0-1 give A000012.

Cf. A294699.

Sequence in context: A173504 A322621 A309036 * A174918 A154991 A090163

Adjacent sequences: A294753 A294754 A294755 * A294757 A294758 A294759

Keyword

nonn,tabl

Author

Seiichi Manyama, Nov 08 2017

Status

approved