A284500 Expansion of Product_{k>=0} (1 - x^(7*k+2)) in powers of x.

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

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)): A284499 (m=1), this sequence (m=2), A284501 (m=3), A284502 (m=4), A284503 (m=5), A284504 (m=6).

Cf. A281458.

Programs

Maple

S:= series(mul(1-x^(7*k+2),k=0..(100-2)/7),x,101):
seq(coeff(S,x,i),i=0..100); # Robert Israel, Jan 17 2023

Mathematica

CoefficientList[Series[Product[1 - x^(7k + 2), {k, 0, 100}], {x, 0, 100}], x] (* Indranil Ghosh, Mar 28 2017 *)

PARI

Vec(prod(k=0, 100, 1 - x^(7*k + 2)) + O(x^101)) \\ Indranil Ghosh, Mar 28 2017

Formula

a(n) = -(1/n)*Sum_{k=1..n} A284443(k)*a(n-k), a(0) = 1.