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Vaclav Kotesovec, <a href="/A293304/b293304.txt">Table of n, a(n) for n = 0..2000</a>

allocated for Vaclav Kotesovec

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

1, 1, 2, 1, 1, 3, 3, 5, 6, 4, 6, 8, 11, 13, 13, 18, 19, 23, 29, 32, 35, 40, 48, 51, 65, 78, 86, 96, 102, 121, 142, 162, 179, 199, 220, 251, 289, 323, 359, 395, 450, 499, 562, 631, 695, 762, 840, 952, 1055, 1167, 1292, 1413, 1557, 1733, 1903, 2112, 2323, 2534

0,3

a(n) ~ c^(1/4) * exp(sqrt(2*c*n)) / (2^(5/4) * sqrt(Pi) * n^(3/4)), where c = -polylog(2, -1/2 + I*sqrt(7)/2) - polylog(2, -1/2 - I*sqrt(7)/2) = 1.323865936864425754643630663383779192757247984691212163137...

nmax = 100; CoefficientList[Series[Product[(1 + x^(2*k-1) + 2*x^(4*k-2)), {k, 1, nmax}], {x, 0, nmax}], x]

Cf. A293072.

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nonn

Vaclav Kotesovec, Oct 05 2017

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allocated for Vaclav Kotesovec

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