A294580 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.

1, 1, -1, 1, -1, -2, 1, -1, -4, -1, 1, -1, -8, -5, 0, 1, -1, -16, -19, -3, 4, 1, -1, -32, -65, -21, 23, 4, 1, -1, -64, -211, -111, 139, 44, 7, 1, -1, -128, -665, -525, 863, 448, 104, 3, 1, -1, -256, -2059, -2343, 5419, 4316, 1414, 70, -2, 1, -1, -512, -6305, -10101, 34103, 40024, 18164, 1206, -93, -9

Offset

0,6

Links

Seiichi Manyama, Antidiagonals n = 0..139, flattened

Formula

A(0,k) = 1 and A(n,k) = -(1/n) * Sum_{j=1..n} (Sum_{d|j} d^(2+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, -4,  -8,  -16,  -32, ...
   -1, -5, -19,  -65, -211, ...
    0, -3, -21, -111, -525, ...

Crossrefs

Columns k=0..2 give A073592, A266964, A294581.

Rows n=0..3 give A000012, (-1)*A000012, (-1)*A000079(n+1), (-1)*A001047(n+1).

Cf. A292166, A294582.

Sequence in context: A205553 A178411 A257598 * A294587 A064645 A285425

Adjacent sequences: A294577 A294578 A294579 * A294581 A294582 A294583

Keyword

sign,tabl,look

Author

Seiichi Manyama, Nov 02 2017

Status

approved