A294583 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*x^j)^(j^k).

1, 1, -1, 1, -1, -1, 1, -1, -4, 0, 1, -1, -16, -5, 0, 1, -1, -64, -65, -3, 1, 1, -1, -256, -665, -79, 23, 0, 1, -1, -1024, -6305, -1575, 831, 44, 1, 1, -1, -4096, -58025, -28255, 33335, 4789, 104, 0, 1, -1, -16384, -527345, -481623, 1323807, 411664, 15099, 70, 0

Offset

0,9

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, ...
   -1, -4, -16,   -64,   -256, ...
    0, -5, -65,  -665,  -6305, ...
    0, -3, -79, -1575, -28255, ...

Crossrefs

Columns k=0..2 give A010815, A266964, A294584.

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

Cf. A294585.

Sequence in context: A324563 A186372 A200893 * A283675 A294653 A126222

Adjacent sequences: A294580 A294581 A294582 * A294584 A294585 A294586

Keyword

sign,tabl

Author

Seiichi Manyama, Nov 03 2017

Status

approved