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%I #12 Aug 22 2017 06:43:59
%S 1,1,3,21,172,1557,14937,148870,1523150,15874211,167584946,1784250269,
%T 19082848084,204183773733,2174724531143,22887441573480,
%U 235016048710027,2294441979279215,19936497820248076,118333942636382173,-709004900481995789,-49850788347995316262
%N G.f. A(x) satisfies: x = Sum_{n>=1} 1/A(x)^(5*n) * Product_{k=1..n} (1 - 1/A(x)^(2*k-1)).
%H Vaclav Kotesovec, <a href="/A247480/b247480.txt">Table of n, a(n) for n = 0..260</a>
%F a(n) ~ c * 12^n * n^(n-2) / (exp(n) * Pi^(2*n)), where c = -sqrt(6) * Pi^3 * exp(5*Pi^2/24)/24 = -24.7341070998048267... - _Vaclav Kotesovec_, Dec 01 2014, updated Aug 22 2017
%t nmax = 20; aa = ConstantArray[0,nmax]; aa[[1]] = 1; Do[AGF = 1+Sum[aa[[n]]*x^n,{n,1,j-1}]+koef*x^j; sol=Solve[SeriesCoefficient[Sum[Product[(1-1/AGF^(2m-1))/AGF^5,{m,1,k}],{k,1,j}],{x,0,j}]==0,koef][[1]]; aa[[j]]=koef/.sol[[1]],{j,2,nmax}]; Flatten[{1,aa}]
%Y Cf. A247482 (exponent=0), A247481 (exponent=1), A249934 (exponent=3), A214692 (exponent=4), A214693 (exponent=6), A214694 (exponent=8), A214695 (exponent=10).
%Y Cf. A214690, A214670.
%K sign
%O 0,3
%A _Vaclav Kotesovec_, Dec 01 2014
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