A374019 - OEIS

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A374019

Expansion of Product_{k>=1} 1 / (1 - x^(4*k-1))^2.

1, 0, 0, 2, 0, 0, 3, 2, 0, 4, 4, 2, 5, 6, 7, 8, 8, 12, 15, 12, 17, 26, 23, 24, 37, 40, 39, 50, 62, 66, 74, 86, 101, 116, 122, 144, 175, 184, 202, 246, 274, 294, 340, 388, 432, 480, 533, 610, 684, 742, 835, 956, 1045, 1144, 1299, 1450, 1586, 1758, 1965, 2182, 2400, 2638, 2941, 3268, 3560, 3922

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Table of n, a(n) for n=0..65.

FORMULA

a(0) = 1; a(n) = (2/n) * Sum_{k=1..n} A050452(k) * a(n-k).

a(n) = Sum_{k=0..n} A035462(k) * A035462(n-k).

a(n) ~ Pi^(3/2) * exp(Pi*sqrt(n/3)) / (2*sqrt(3) * Gamma(1/4)^2 * n). - Vaclav Kotesovec, Jun 25 2024

MATHEMATICA

nmax = 65; CoefficientList[Series[Product[1/(1 - x^(4 k - 1))^2, {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS