A284503 Expansion of Product_{k>=0} (1 - x^(7*k+5)) in powers of x.

1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 2, 0, -1, 0, 0, -1, 0, 2, 0, -1, 0, 0, -1, 0, 3, 0, -1, 0, 0, -2, 0, 3, 0, -1, 0, 0, -3, 0, 4, 0, -1, 1, 0, -4, 0, 4, 0, -1, 1, 0, -5, 0, 5, 0, -1, 2, 0, -7, 0, 5, 0

Offset: 0

Author

Seiichi Manyama, Mar 28 2017

Keywords

• sign
• look

Links

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

Crossrefs

Cf. Product_{k>=0} (1 - x^(7*k+m)): A284499 (m=1), A284500 (m=2), A284501 (m=3), A284502 (m=4), this sequence (m=5), A284504 (m=6).

Cf. A281455.

Programs

Mathematica

CoefficientList[Series[Product[1 - x^(7k + 5), {k, 0, 100}], {x, 0, 100}], x] (* Indranil Ghosh, Mar 28 2017  *)

PARI

Vec(prod(k=0, 100, 1 - x^(7*k + 5)) + O(x^101)) \\ Indranil Ghosh, Mar 28 2017

Formula

a(n) = -(1/n) * Sum_{k=1..n} A284446(k) * a(n-k), a(0) = 1.