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A285460 Expansion of Product_{k>=1} ((1 + x^(4*k)) / (1 - x^k))^k. 6
1, 1, 3, 6, 14, 25, 51, 92, 175, 308, 554, 957, 1670, 2820, 4778, 7940, 13169, 21511, 35032, 56405, 90453, 143716, 227342, 356950, 557977, 866588, 1340109, 2060912, 3156274, 4810016, 7301490, 11034661, 16614681, 24916208, 37234864, 55440054, 82274277 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) ~ exp(1/12 + 3 * 2^(-8/3) * (67*Zeta(3))^(1/3) * n^(2/3)) * (67*Zeta(3))^(7/36) / (A * 2^(14/9) * sqrt(3*Pi) * n^(25/36)), where A is the Glaisher-Kinkelin constant A074962.
MATHEMATICA
nmax = 40; CoefficientList[Series[Product[((1+x^(4*k))/(1-x^k))^k, {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
Sequence in context: A026271 A166212 A291988 * A236429 A316245 A002219
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Apr 19 2017
STATUS
approved

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Last modified July 15 19:27 EDT 2024. Contains 374334 sequences. (Running on oeis4.)