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%I #11 May 08 2017 00:21:56
%S 1,1,9,35,131,454,1601,5325,17467,55588,173858,532809,1607056,4769263,
%T 13957660,40302923,114962909,324157109,904247056,2496917319,
%U 6829241131,18510038697,49741367504,132582175873,350655140642,920568519505,2399692063845,6213105691838,15982216140168,40855658807127,103814659491641
%N Expansion of Product_{k>=1} 1/(1 - x^k)^(k*(k+1)*(5*k-2)/6).
%C Euler transform of the heptagonal pyramidal numbers (A002413).
%H Vaclav Kotesovec, <a href="/A279218/b279218.txt">Table of n, a(n) for n = 0..1000</a>
%H M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
%H M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HeptagonalPyramidalNumber.html">Heptagonal Pyramidal Number</a>
%H <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal numbers</a>
%F G.f.: Product_{k>=1} 1/(1 - x^k)^(k*(k+1)*(5*k-2)/6).
%F a(n) ~ exp(-Zeta'(-1)/3 - Zeta(3)/(8*Pi^2) - Pi^16/(388800000000*Zeta(5)^3) - Pi^8*Zeta(3)/(5400000*Zeta(5)^2) - Zeta(3)^2/(450*Zeta(5)) + 5*Zeta'(-3)/6 + (Pi^12/(270000000*2^(2/5)*5^(1/5)*Zeta(5)^(11/5)) + Pi^4*Zeta(3)/(4500*2^(2/5) * 5^(1/5)*Zeta(5)^(6/5))) * n^(1/5) + (-Pi^8/(180000*2^(4/5)*5^(2/5)*Zeta(5)^(7/5)) - Zeta(3)/(3*2^(4/5)*(5*Zeta(5))^(2/5))) * n^(2/5) + (Pi^4/(180*2^(1/5)*(5*Zeta(5))^(3/5))) * n^(3/5) + ((5*(5*Zeta(5))^(1/5))/(2^(8/5))) * n^(4/5)) * Zeta(5)^(67/720) / (2^(113/360) * 5^(293/720) * sqrt(Pi) * n^(427/720)). - _Vaclav Kotesovec_, Dec 08 2016
%t nmax=30; CoefficientList[Series[Product[1/(1 - x^k)^(k (k + 1) (5 k - 2)/6), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A000335, A002413, A279215, A279216, A279217, A279219.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Dec 08 2016
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