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 A255612 G.f.: Product_{k>=1} 1/(1-x^k)^(5*k). 9
 1, 5, 25, 100, 370, 1251, 4005, 12150, 35400, 99365, 270353, 715025, 1844650, 4652075, 11494605, 27872056, 66428295, 155809600, 360079225, 820715820, 1846583863, 4104572975, 9019869125, 19608423750, 42193733645, 89917531549, 189863358445, 397401303850 (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)^(5*k). a(n) ~ 5^(11/36) * Zeta(3)^(11/36) * exp(5/12 + 3 * 2^(-2/3) * 5^(1/3) * Zeta(3)^(1/3) * n^(2/3)) / (A^5 * 2^(7/36) * sqrt(3*Pi) * n^(29/36)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant and Zeta(3) = A002117 = 1.202056903... . - Vaclav Kotesovec, Feb 28 2015 G.f.: exp(5*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, 5*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)^(5*k), {k, 1, nmax}], {x, 0, nmax}], x] CROSSREFS Cf. A000219, A161870, A255610, A255611, A255613, A255614, A193427. Column k=5 of A255961. Sequence in context: A201841 A146830 A316778 * A022729 A098111 A224415 Adjacent sequences:  A255609 A255610 A255611 * A255613 A255614 A255615 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 November 29 21:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)