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A326780
E.g.f.: Product_{k>=1} 1/(1 - x^(4*k-3)/(4*k-3)).
4
1, 1, 2, 6, 24, 144, 864, 6048, 48384, 475776, 4902912, 53932032, 647184384, 8892398592, 126430875648, 1906924529664, 30510792474624, 539606261956608, 9890452422918144, 188459240926150656, 3773077461736095744, 81667528704634650624, 1819516013302975561728
OFFSET
0,3
LINKS
D. H. Lehmer, On reciprocally weighted partitions, Acta Arithmetica XXI (1972), 379-388 (Theorem 7).
FORMULA
a(n) ~ 2^(7/2) * exp(-gamma/4) * n^(1/4) * n! / Gamma(1/4)^2, where gamma is the Euler-Mascheroni constant A001620 and Gamma() is the Gamma function [Lehmer, 1972].
MATHEMATICA
nmax = 25; CoefficientList[Series[1/Product[(1-x^(4*k-3)/(4*k-3)), {k, 1, Floor[nmax/4] + 1}], {x, 0, nmax}], x] * Range[0, nmax]!
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jul 24 2019
STATUS
approved