A375061 Expansion of 1 / Sum_{k in Z} x^(2*k) / (1 - x^(5*k+2)).

1, 1, -1, -3, -1, 5, 5, -5, -13, -2, 21, 20, -18, -46, -8, 66, 62, -54, -135, -21, 188, 172, -147, -361, -57, 479, 433, -364, -882, -133, 1147, 1024, -850, -2039, -309, 2583, 2286, -1880, -4466, -662, 5573, 4889, -3987, -9403, -1392, 11541, 10059, -8147, -19087, -2794

Offset: 0

Author

Seiichi Manyama, Jul 29 2024

Keywords

• sign

Crossrefs

Convolution inverse of A340455.

Cf. A375062, A375063, A375064.

Programs

PARI

my(N=50, x='x+O('x^N)); Vec(1/sum(k=-N, N, x^(2*k)/(1-x^(5*k+2))))

PARI

my(N=50, x='x+O('x^N)); Vec(prod(k=1, N, ((1-x^(5*k-2))*(1-x^(5*k-3)))^3/((1-x^k)*(1-x^(5*k)))))

Formula

G.f.: Product_{k>0} ((1-x^(5*k-2)) * (1-x^(5*k-3)))^3 / ((1-x^k) * (1-x^(5*k))).