A294699 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1-j^(k*j)*x^j)^j(k*j) in powers of x.

1, 1, -1, 1, -1, -1, 1, -1, -16, 0, 1, -1, -256, -713, 0, 1, -1, -4096, -531185, -64711, 1, 1, -1, -65536, -387416393, -4294405135, -9688521, 0, 1, -1, -1048576, -282429470945, -281474581032631, -95363000655153, -2165724176, 1, 1

Offset

0,9

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, ...
   -1,    -16,        -256,            -4096, ...
    0,   -713,     -531185,       -387416393, ...
    0, -64711, -4294405135, -281474581032631, ...

Crossrefs

Columns k=0..1 give A010815, A294704.

Rows n=0..1 give A000012, (-1)*A000012.

Cf. A294583, A294653, A294756.

Sequence in context: A187585 A228574 A007791 * A326852 A070570 A347158

Adjacent sequences: A294696 A294697 A294698 * A294700 A294701 A294702

Keyword

sign,tabl

Author

Seiichi Manyama, Nov 07 2017

Status

approved