A283675 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1-x^j)^(j^(k*j)) in powers of x.

1, 1, -1, 1, -1, -1, 1, -1, -4, 0, 1, -1, -16, -23, 0, 1, -1, -64, -713, -223, 1, 1, -1, -256, -19619, -64687, -2767, 0, 1, -1, -1024, -531185, -16755517, -9688545, -42268, 1, 1, -1, -4096, -14347883, -4294403215, -30499543213, -2165715003, -759008, 0, 1, -1, -16384

Offset

0,9

Links

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

Formula

G.f. of column k: Product_{j>=1} (1-x^j)^(j^(k*j)).

A(0,k) = 1 and A(n,k) = -(1/n) * Sum_{j=1..n} (Sum_{d|j} d^(k*d+1)) * A(n-j,k) for n > 0. - Seiichi Manyama, Nov 04 2017

Example

Square array begins:
   1,    1,      1,         1, ...
  -1,   -1,     -1,        -1, ...
  -1,   -4,    -16,       -64, ...
   0,  -23,   -713,    -19619, ...
   0, -223, -64687, -16755517, ...

Crossrefs

Columns k=0..4 give A010815, A283499, A283534, A283536, A283803.

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

Main diagonal gives A283720.

Cf. A283674.

Sequence in context: A186372 A200893 A294583 * A294653 A126222 A071637

Adjacent sequences: A283672 A283673 A283674 * A283676 A283677 A283678

Keyword

sign,tabl

Author

Seiichi Manyama, Mar 14 2017

Status

approved