A375063 Expansion of 1 / Sum_{k in Z} x^k / (1 - x^(5*k+2)).

1, -1, 0, 0, -1, 3, -3, 1, 0, -3, 9, -9, 3, 1, -9, 22, -22, 9, 2, -22, 51, -51, 22, 6, -51, 108, -108, 50, 13, -108, 221, -221, 105, 29, -220, 429, -429, 212, 57, -426, 810, -810, 407, 113, -801, 1479, -1478, 759, 208, -1457, 2640, -2637, 1371, 381, -2589, 4598, -4590, 2419, 669

Offset: 0

Author

Seiichi Manyama, Jul 29 2024

Keywords

• sign

Crossrefs

Convolution inverse of A340453.

Cf. A375061, A375062, A375064.

Programs

PARI

my(N=60, x='x+O('x^N)); Vec(1/sum(k=-N, N, x^k/(1-x^(5*k+2))))

PARI

my(N=60, x='x+O('x^N)); Vec(prod(k=1, N, (1-x^(5*k-1))*(1-x^(5*k-4))/(1-x^(5*k))^2))

Formula

G.f.: Product_{k>0} (1-x^(5*k-1)) * (1-x^(5*k-4)) / (1-x^(5*k))^2.