A376712 - OEIS

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A376712

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

1, 1, 4, 10, 21, 39, 70, 120, 205, 342, 568, 924, 1490, 2356, 3684, 5666, 8619, 12935, 19230, 28280, 41260, 59680, 85740, 122306, 173447, 244472, 342774, 478014, 663391, 916149, 1259526, 1723772, 2349209, 3188160, 4309660, 5803002, 7785040, 10406296, 13862404

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..38.

FORMULA

a(n) ~ exp(2*Pi*sqrt(2*n/5)) / (5^(5/4) * (sqrt(5)-1)^2 * n^(3/2)).

MATHEMATICA

nmax = 40; CoefficientList[Series[Sum[x^(k^2)/Product[1-x^j, {j, 1, k}]^4, {k, 0, Sqrt[nmax]}], {x, 0, nmax}], x]

CROSSREFS

Cf. A003114, A000041, A376709.

Sequence in context: A023538 A085360 A265050 * A243738 A258352 A024988

Adjacent sequences: A376709 A376710 A376711 * A376713 A376714 A376715

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Oct 02 2024

STATUS

approved