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A255614 G.f.: Product_{k>=1} 1/(1-x^k)^(7*k).

%I A255614 #20 Feb 16 2025 08:33:25
%S A255614 1,7,42,203,882,3486,12880,44885,149170,475587,1462993,4359474,
%T A255614 12628091,35656446,98372109,265701212,703800790,1830960824,4684293222,
%U A255614 11798774953,29288385021,71714795158,173351031721,413964243476,977243358574,2281942600035,5273570826594
%N A255614 G.f.: Product_{k>=1} 1/(1-x^k)^(7*k).
%H A255614 Vaclav Kotesovec, <a href="/A255614/b255614.txt">Table of n, a(n) for n = 0..1000</a>
%H A255614 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 A255614 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PlanePartition.html">Plane Partition</a>
%H A255614 Wikipedia, <a href="http://en.wikipedia.org/wiki/Plane_partition">Plane partition</a>
%F A255614 G.f.: Product_{k>=1} 1/(1-x^k)^(7*k).
%F A255614 a(n) ~ 7^(13/36) * Zeta(3)^(13/36) * exp(7/12 + 3 * 2^(-2/3) * 7^(1/3) * Zeta(3)^(1/3) * n^(2/3)) / (A^7 * 2^(5/36) * sqrt(3*Pi) * n^(31/36)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant and Zeta(3) = A002117 = 1.202056903... . - _Vaclav Kotesovec_, Feb 28 2015
%F A255614 G.f.: exp(7*Sum_{k>=1} x^k/(k*(1 - x^k)^2)). - _Ilya Gutkovskiy_, May 29 2018
%p A255614 a:= proc(n) option remember; `if`(n=0, 1, 7*add(
%p A255614       a(n-j)*numtheory[sigma][2](j), j=1..n)/n)
%p A255614     end:
%p A255614 seq(a(n), n=0..30);  # _Alois P. Heinz_, Mar 11 2015
%t A255614 nmax=50; CoefficientList[Series[Product[1/(1-x^k)^(7*k),{k,1,nmax}],{x,0,nmax}],x]
%Y A255614 Cf. A000219, A161870, A255610, A255611, A255612, A255613, A193427.
%Y A255614 Column k=7 of A255961.
%K A255614 nonn
%O A255614 0,2
%A A255614 _Vaclav Kotesovec_, Feb 28 2015
%E A255614 New name from _Vaclav Kotesovec_, Mar 12 2015