A284317 Expansion of Product_{k>=0} (1 - x^(5*k+4)) in powers of x.

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

Offset: 0

Author

Seiichi Manyama, Mar 25 2017

Keywords

• sign

Links

• Robert Israel, 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), A284316 (m=4), this sequence (m=5).

Cf. A281243, A284103.

Programs

Maple

S:= series(mul(1-x^(5*k+4),k=0..200),x,101):
seq(coeff(S,x,j),j=0..100); # Robert Israel, Mar 27 2017

Mathematica

CoefficientList[Series[Product[1 - x^(5k + 4), {k, 0, 100}], {x, 0, 100}], x] (* Indranil Ghosh, Mar 25 2017 *)

PARI

Vec(prod(k=0, 100, 1 - x^(5*k + 4)) + O(x^101)) \\ Indranil Ghosh, Mar 25 2017

Formula

a(n) = -(1/n)*Sum_{k=1..n} A284103(k)*a(n-k), a(0) = 1.

G.f. is the QPochhammer symbol (x^4;x^5)infinity. - _Robert Israel, Mar 27 2017