A284316 Expansion of Product_{k>=0} (1 - x^(4*k+3)) in powers of x.

1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 2, -1, 0, -1, 2, -1, 0, -1, 3, -1, 0, -2, 3, -1, 0, -3, 4, -1, 1, -4, 4, -1, 1, -5, 5, -1, 2, -7, 5, -1, 3, -8, 6, -1, 5, -10, 6, -2, 6, -12, 7, -2, 9, -14, 7, -3, 11, -16, 8, -4, 15, -19, 8, -6, 18, -21, 9

Offset: 0

Author

Seiichi Manyama, Mar 25 2017

Keywords

• sign
• easy

Links

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

Crossrefs

Cf. Product_{k>=0} (1 - x^(m*k+m-1)): A081362 (m=2), A284315 (m=3), this sequence (m=4), A284317 (m=5).

Cf. A050452, A147599, A284313, A111330.

Programs

Mathematica

CoefficientList[Series[Product[1 - x^(4k + 3), {k, 0, 100}], {x, 0, 100}], x] (* Indranil Ghosh, Mar 25 2017 *)

PARI

Vec(prod(k=0, 100, 1 - x^(4*k+3)) + O(x^101)) \\ Indranil Ghosh, Mar 25 2017

Formula

a(n) = -(1/n)*Sum_{k=1..n} A050452(k)*a(n-k), a(0) = 1.

O.g.f.: Sum_{n >= 0} (-1)^n*x^(n*(2*n+1)) / Product_{k = 1..n} ( 1 - x^(4*k) ). Cf. A284313. - Peter Bala, Nov 28 2020