A294587 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1 - j*x^j)^(j^k).

1, 1, -1, 1, -1, -2, 1, -1, -4, -1, 1, -1, -8, -5, -1, 1, -1, -16, -19, -3, 5, 1, -1, -32, -65, -13, 23, 1, 1, -1, -64, -211, -63, 131, 44, 13, 1, -1, -128, -665, -301, 815, 497, 104, 4, 1, -1, -256, -2059, -1383, 5195, 4840, 1149, 70, 0, 1, -1, -512, -6305, -6133, 33143, 45021, 13752, 662, -93, 2

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^(k+1+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, ...
   -1, -3, -13, -63, -301, ...

Crossrefs

Columns k=0..2 give A022661, A266964, A294588.

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

Cf. A283272.

Sequence in context: A178411 A257598 A294580 * A064645 A285425 A008307

Adjacent sequences: A294584 A294585 A294586 * A294588 A294589 A294590

Keyword

sign,tabl

Author

Seiichi Manyama, Nov 03 2017

Status

approved