A376581 - OEIS

A376581

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

1, 1, 2, 3, 5, 7, 9, 13, 17, 22, 30, 38, 48, 62, 78, 97, 122, 151, 184, 228, 278, 335, 408, 491, 588, 707, 843, 1000, 1189, 1407, 1658, 1955, 2295, 2686, 3145, 3670, 4270, 4968, 5763, 6671, 7720, 8909, 10263, 11816, 13577, 15574, 17850, 20424, 23333, 26638, 30365

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OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

FORMULA

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

MATHEMATICA

nmax=100; CoefficientList[Series[Sum[x^(k^2)/Product[1-x^(2*j-1), {j, 1, k}]^2, {k, 0, Sqrt[nmax]}], {x, 0, nmax}], x]

CROSSREFS

Cf. A053264, A306734, A340647, A376542, A376580.

Sequence in context: A354531 A302835 A200672 * A341497 A332686 A069999

Adjacent sequences: A376578 A376579 A376580 * A376582 A376583 A376584

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Sep 29 2024

STATUS

approved