A284320 Expansion of Product_{k>=0} (1 - x^(5*k+3)) in powers of x.

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

Offset: 0

Author

Seiichi Manyama, Mar 25 2017

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. Product_{k>=0} (1 - x^(5*k+m)): A284314 (m=1), A284319 (m=2), this sequence (m=3), A284317 (m=4).

Cf. A281271, A284281.

Programs

Mathematica

CoefficientList[Series[Product[1 - x^(5k + 3), {k, 0, 100}], {x, 0, 100}], x] (* Indranil Ghosh, Mar 25 2017 *) (* or *)
a[0]=1; a[n_]:=a[n]= -(1/n) Sum[ a[n-k] DivisorSum[k, # &, Mod[#,5] == 3 &], {k, n}]; a /@ Range[0, 100] (* Giovanni Resta, Mar 25 2017 *)

PARI

Vec(prod(k=0, 100, 1 - x^(5*k + 3)) + O(x^101)) \\ Indranil Ghosh, Mar 25 2017

Formula

a(n) = -(1/n)*Sum_{k=1..n} A284281(k)*a(n-k), a(0) = 1.