OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
Vaclav Kotesovec, A method of finding the asymptotics of q-series based on the convolution of generating functions, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 19.
Eric Weisstein's World of Mathematics, Plane Partition
Wikipedia, Plane partition
FORMULA
G.f.: Product_{k>=1} 1/(1-x^k)^(4*k).
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
G.f.: exp(4*Sum_{k>=1} x^k/(k*(1 - x^k)^2)). - Ilya Gutkovskiy, May 29 2018
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, 4*add(
a(n-j)*numtheory[sigma][2](j), j=1..n)/n)
end:
seq(a(n), n=0..30); # Alois P. Heinz, Mar 11 2015
MATHEMATICA
nmax=50; CoefficientList[Series[Product[1/(1-x^k)^(4*k), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Feb 28 2015
EXTENSIONS
New name from Vaclav Kotesovec, Mar 12 2015
STATUS
approved