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

1, 7, 42, 203, 882, 3486, 12880, 44885, 149170, 475587, 1462993, 4359474, 12628091, 35656446, 98372109, 265701212, 703800790, 1830960824, 4684293222, 11798774953, 29288385021, 71714795158, 173351031721, 413964243476, 977243358574, 2281942600035, 5273570826594

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)^(7*k).

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

G.f.: exp(7*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, 7*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)^(7*k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000219, A161870, A255610, A255611, A255612, A255613, A193427.

Column k=7 of A255961.

Sequence in context: A073376 A094429 A246434 * A022731 A092072 A319890

Adjacent sequences: A255611 A255612 A255613 * A255615 A255616 A255617

Keyword

nonn

Author

Vaclav Kotesovec, Feb 28 2015

Extensions

New name from Vaclav Kotesovec, Mar 12 2015

Status

approved