A375064 Expansion of 1 / Sum_{k in Z} x^(3*k) / (1 - x^(5*k+1)).

1, 0, -1, -1, 0, 3, 0, -3, -3, 1, 9, 1, -9, -9, 3, 22, 3, -22, -22, 9, 51, 8, -51, -51, 21, 108, 19, -108, -108, 48, 221, 42, -221, -221, 99, 429, 86, -429, -428, 199, 810, 170, -809, -807, 378, 1479, 321, -1476, -1470, 702, 2640, 589, -2631, -2618, 1258, 4599, 1050, -4577, -4548, 2211

Offset: 0

Author

Seiichi Manyama, Jul 29 2024

Keywords

• sign

Crossrefs

Convolution inverse of A340454.

Cf. A375061, A375062, A375063.

Programs

PARI

my(N=60, x='x+O('x^N)); Vec(1/sum(k=-N, N, x^(3*k)/(1-x^(5*k+1))))

PARI

my(N=60, x='x+O('x^N)); Vec(prod(k=1, N, (1-x^(5*k-2))*(1-x^(5*k-3))/(1-x^(5*k))^2))

Formula

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