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A255611 G.f.: Product_{k>=1} 1/(1-x^k)^(4*k). 9

%I

%S 1,4,18,64,215,660,1938,5400,14527,37728,95278,234344,563506,1326796,

%T 3066040,6963048,15564661,34282360,74486376,159785472,338703796,

%U 709957616,1472529670,3023894672,6151408852,12402137024,24792822174,49162962280,96737562642

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

%H Vaclav Kotesovec, <a href="/A255611/b255611.txt">Table of n, a(n) for n = 0..1000</a>

%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PlanePartition.html">Plane Partition</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Plane_partition">Plane partition</a>

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

%F 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 G.f.: exp(4*Sum_{k>=1} x^k/(k*(1 - x^k)^2)). - _Ilya Gutkovskiy_, May 29 2018

%p a:= proc(n) option remember; `if`(n=0, 1, 4*add(

%p a(n-j)*numtheory[sigma][2](j), j=1..n)/n)

%p end:

%p seq(a(n), n=0..30); # _Alois P. Heinz_, Mar 11 2015

%t nmax=50; CoefficientList[Series[Product[1/(1-x^k)^(4*k),{k,1,nmax}],{x,0,nmax}],x]

%Y Cf. A000219, A161870, A255610, A255612, A255613, A255614, A193427.

%Y Column k=4 of A255961.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Feb 28 2015

%E New name from _Vaclav Kotesovec_, Mar 12 2015

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Last modified October 18 01:04 EDT 2019. Contains 328135 sequences. (Running on oeis4.)