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%I #6 Jul 24 2019 18:09:19
%S 1,1,2,6,24,144,864,6048,48384,475776,4902912,53932032,647184384,
%T 8892398592,126430875648,1906924529664,30510792474624,539606261956608,
%U 9890452422918144,188459240926150656,3773077461736095744,81667528704634650624,1819516013302975561728
%N E.g.f.: Product_{k>=1} 1/(1 - x^(4*k-3)/(4*k-3)).
%H Vaclav Kotesovec, <a href="/A326780/b326780.txt">Table of n, a(n) for n = 0..447</a>
%H D. H. Lehmer, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa21/aa21123.pdf">On reciprocally weighted partitions</a>, Acta Arithmetica XXI (1972), 379-388 (Theorem 7).
%F 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].
%t 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]!
%Y Cf. A007841, A294506, A309319, A326755, A326756, A326779.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Jul 24 2019
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