A284499 Expansion of Product_{k>=0} (1 - x^(7*k+1)) in powers of x.

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

Offset: 0

Author

Seiichi Manyama, Mar 28 2017

Keywords

• sign
• look

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. Product_{k>=0} (1 - x^(7*k+m)): this sequence (m=1), A284500 (m=2), A284501 (m=3), A284502 (m=4), A284503 (m=5), A284504 (m=6).

Cf. A280457.

Programs

Maple

G:= mul(1-x^(7*k+1),k=0..100/7):
S:= series(G,x,101):
seq(coeff(S,x,j),j=0..100); # Robert Israel, Mar 29 2017

Mathematica

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

PARI

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

Formula

a(n) = -(1/n)*Sum_{k=1..n} A284099(k)*a(n-k), a(0) = 1.