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A255612 G.f.: Product_{k>=1} 1/(1-x^k)^(5*k).

%I A255612 #20 Feb 16 2025 08:33:25
%S A255612 1,5,25,100,370,1251,4005,12150,35400,99365,270353,715025,1844650,
%T A255612 4652075,11494605,27872056,66428295,155809600,360079225,820715820,
%U A255612 1846583863,4104572975,9019869125,19608423750,42193733645,89917531549,189863358445,397401303850
%N A255612 G.f.: Product_{k>=1} 1/(1-x^k)^(5*k).
%H A255612 Vaclav Kotesovec, <a href="/A255612/b255612.txt">Table of n, a(n) for n = 0..1000</a>
%H A255612 Vaclav Kotesovec, <a href="http://arxiv.org/abs/1509.08708">A method of finding the asymptotics of q-series based on the convolution of generating functions</a>, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 19.
%H A255612 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PlanePartition.html">Plane Partition</a>
%H A255612 Wikipedia, <a href="http://en.wikipedia.org/wiki/Plane_partition">Plane partition</a>
%F A255612 G.f.: Product_{k>=1} 1/(1-x^k)^(5*k).
%F A255612 a(n) ~ 5^(11/36) * Zeta(3)^(11/36) * exp(5/12 + 3 * 2^(-2/3) * 5^(1/3) * Zeta(3)^(1/3) * n^(2/3)) / (A^5 * 2^(7/36) * sqrt(3*Pi) * n^(29/36)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant and Zeta(3) = A002117 = 1.202056903... . - _Vaclav Kotesovec_, Feb 28 2015
%F A255612 G.f.: exp(5*Sum_{k>=1} x^k/(k*(1 - x^k)^2)). - _Ilya Gutkovskiy_, May 29 2018
%p A255612 a:= proc(n) option remember; `if`(n=0, 1, 5*add(
%p A255612       a(n-j)*numtheory[sigma][2](j), j=1..n)/n)
%p A255612     end:
%p A255612 seq(a(n), n=0..30);  # _Alois P. Heinz_, Mar 11 2015
%t A255612 nmax=50; CoefficientList[Series[Product[1/(1-x^k)^(5*k),{k,1,nmax}],{x,0,nmax}],x]
%Y A255612 Cf. A000219, A161870, A255610, A255611, A255613, A255614, A193427.
%Y A255612 Column k=5 of A255961.
%K A255612 nonn
%O A255612 0,2
%A A255612 _Vaclav Kotesovec_, Feb 28 2015
%E A255612 New name from _Vaclav Kotesovec_, Mar 12 2015