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A255611 G.f.: Product_{k>=1} 1/(1-x^k)^(4*k).

%I A255611 #23 Feb 16 2025 08:33:25
%S A255611 1,4,18,64,215,660,1938,5400,14527,37728,95278,234344,563506,1326796,
%T A255611 3066040,6963048,15564661,34282360,74486376,159785472,338703796,
%U A255611 709957616,1472529670,3023894672,6151408852,12402137024,24792822174,49162962280,96737562642
%N A255611 G.f.: Product_{k>=1} 1/(1-x^k)^(4*k).
%H A255611 Vaclav Kotesovec, <a href="/A255611/b255611.txt">Table of n, a(n) for n = 0..1000</a>
%H A255611 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 A255611 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PlanePartition.html">Plane Partition</a>
%H A255611 Wikipedia, <a href="http://en.wikipedia.org/wiki/Plane_partition">Plane partition</a>
%F A255611 G.f.: Product_{k>=1} 1/(1-x^k)^(4*k).
%F A255611 a(n) ~ 2^(1/3) * Zeta(3)^(5/18) * exp(1/3 + 3 * Zeta(3)^(1/3) * n^(2/3)) / (A^4 * sqrt(3*Pi) * n^(7/9)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant and Zeta(3) = A002117 = 1.202056903... . - _Vaclav Kotesovec_, Feb 28 2015
%F A255611 G.f.: exp(4*Sum_{k>=1} x^k/(k*(1 - x^k)^2)). - _Ilya Gutkovskiy_, May 29 2018
%p A255611 a:= proc(n) option remember; `if`(n=0, 1, 4*add(
%p A255611       a(n-j)*numtheory[sigma][2](j), j=1..n)/n)
%p A255611     end:
%p A255611 seq(a(n), n=0..30);  # _Alois P. Heinz_, Mar 11 2015
%t A255611 nmax=50; CoefficientList[Series[Product[1/(1-x^k)^(4*k),{k,1,nmax}],{x,0,nmax}],x]
%Y A255611 Cf. A000219, A161870, A255610, A255612, A255613, A255614, A193427.
%Y A255611 Column k=4 of A255961.
%K A255611 nonn
%O A255611 0,2
%A A255611 _Vaclav Kotesovec_, Feb 28 2015
%E A255611 New name from _Vaclav Kotesovec_, Mar 12 2015