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A255613 G.f.: Product_{k>=1} 1/(1-x^k)^(6*k). 8
1, 6, 33, 146, 588, 2160, 7459, 24354, 76071, 228420, 663177, 1868220, 5124224, 13718748, 35932278, 92242982, 232473006, 575971494, 1404600837, 3375138816, 7998932769, 18712911214, 43246451181, 98799885342, 223269183076, 499357990254, 1105934610042 (list; graph; refs; listen; history; text; internal format)
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)^(6*k).

a(n) ~ 2^(1/6) * Zeta(3)^(1/3) * exp(1/2 + 2^(-1/3) * 3^(4/3) * Zeta(3)^(1/3) * n^(2/3)) / (A^6 * 3^(1/6) * sqrt(Pi) * n^(5/6)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant and Zeta(3) = A002117 = 1.202056903... . - Vaclav Kotesovec, Feb 28 2015

G.f.: exp(6*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, 6*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)^(6*k), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A000219, A161870, A255610, A255611, A255612, A255614, A193427.

Column k=6 of A255961.

Sequence in context: A120009 A074087 A297592 * A022730 A266944 A301272

Adjacent sequences:  A255610 A255611 A255612 * A255614 A255615 A255616

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Feb 28 2015

EXTENSIONS

New name from Vaclav Kotesovec, Mar 12 2015

STATUS

approved

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Last modified March 21 10:13 EDT 2019. Contains 321368 sequences. (Running on oeis4.)