A327046 - OEIS

A327046

Expansion of Product_{k>=1} (1 + x^k) * (1 + x^(2*k)) * (1 + x^(3*k)) * (1 + x^(4*k)).

1, 1, 2, 4, 6, 9, 15, 21, 30, 45, 62, 85, 120, 161, 216, 293, 385, 505, 667, 862, 1112, 1438, 1833, 2330, 2965, 3733, 4688, 5887, 7334, 9114, 11319, 13970, 17203, 21162, 25905, 31643, 38605, 46911, 56891, 68904, 83179, 100224, 120603, 144719, 173360, 207396

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OFFSET

0,3

LINKS

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

FORMULA

a(n) ~ sqrt(5) * exp(5*Pi*sqrt(n)/6) / (16*sqrt(3)*n^(3/4)).

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[(1+x^k) * (1+x^(2*k)) * (1+x^(3*k)) * (1+x^(4*k)), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A000009, A001935, A327045, A327047.

Cf. A107742, A327043.