A284314 Expansion of Product_{k>=0} (1 - x^(5*k+1)) in powers of x.

1, -1, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 2, -1, 0, 0, -1, 2, -1, 0, 0, -1, 3, -2, 0, 0, -1, 3, -3, 1, 0, -1, 4, -4, 1, 0, -1, 4, -5, 2, 0, -1, 5, -7, 3, 0, -1, 5, -8, 5, -1, -1, 6, -10, 6, -1, -1, 6, -12, 9, -2, -1, 7, -14, 11, -3, -1, 7, -16, 15, -5

Offset

0,18

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Formula

a(n) = -(1/n)*Sum_{k=1..n} A284097(k)*a(n-k), a(0) = 1.

Mathematica

CoefficientList[Series[Product[1 - x^(5k + 1), {k, 0, 100}], {x, 0, 100}], x] (* Indranil Ghosh, Mar 25 2017 *)

Prog

(PARI) Vec(prod(k=0, 100, 1 - x^(5*k + 1)) + O(x^101)) \\ Indranil Ghosh, Mar 25 2017

Crossrefs

Cf. Product_{k>=0} (1 - x^(m*k+1)): A081362 (m=2), A284312 (m=3), A284313 (m=4), this sequence (m=5).

Cf. A280454, A284097.

Sequence in context: A180981 A284317 A281243 * A280454 A124645 A029409

Adjacent sequences: A284311 A284312 A284313 * A284315 A284316 A284317

Keyword

sign

Author

Seiichi Manyama, Mar 25 2017

Status

approved