A363800 Expansion of Product_{k>0} (1 - x^(7*k-5)) * (1 - x^(7*k-2)) * (1 - x^(7*k)).

1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0

Offset

0

Links

Table of n, a(n) for n=0..98.

Formula

G.f.: Sum_{k in Z} (-1)^k * x^(k * (7*k + 3) / 2).

a(0) = 1; a(n) = -(1/n) * Sum_{k=1..n} A363803(k) * a(n-k).

Prog

(PARI) my(N=100, x='x+O('x^N)); Vec(prod(k=1, N, 1-[1, 0, 1, 0, 0, 1, 0][k%7+1]*x^k))

Crossrefs

Convolution inverse of A346797.

Cf. A232714, A363801.

Cf. A186029, A218471, A363803.

Sequence in context: A179560 A341602 A128407 * A134286 A023531 A320841

Adjacent sequences: A363797 A363798 A363799 * A363801 A363802 A363803

Keyword

sign

Author

Seiichi Manyama, Jun 23 2023

Status

approved