A284319 Expansion of Product_{k>=0} (1 - x^(5*k+2)) in powers of x.

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

Offset: 0

Author

Seiichi Manyama, Mar 25 2017

Keywords

• sign

Crossrefs

Cf. Product_{k>=0} (1 - x^(5*k+m)): A284314 (m=1), this sequence (m=2), A284320 (m=3), A284317 (m=4).

Cf. A281272, A284280.

Programs

Mathematica

CoefficientList[Series[Product[1 - x^(5k + 2), {k, 0, 100}], {x, 0, 100}], x] (* Indranil Ghosh, Mar 25 2017 *)

PARI

Vec(prod(k=0, 100, 1 - x^(5*k + 2)) + O(x^101)) \\ Indranil Ghosh, Mar 25 2017

Formula

a(n) = -(1/n)*Sum_{k=1..n} A284280(k)*a(n-k), a(0) = 1.