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A247482 G.f. A(x) satisfies: x = Sum_{n>=1} Product_{k=1..n} (1 - 1/A(x)^(2*k-1)).

%I A247482 #17 Mar 28 2024 03:20:06
%S A247482 1,1,-2,1,-3,-18,-124,-1174,-12150,-141536,-1816780,-25461723,
%T A247482 -386593670,-6320496592,-110711177281,-2068814967831,-41089562943757,
%U A247482 -864563028340432,-19214971769126974,-449887669808788433,-11069673481210168218,-285604488897863640237
%N A247482 G.f. A(x) satisfies: x = Sum_{n>=1} Product_{k=1..n} (1 - 1/A(x)^(2*k-1)).
%H A247482 Vaclav Kotesovec, <a href="/A247482/b247482.txt">Table of n, a(n) for n = 0..370</a>
%F A247482 a(n) ~ c * 12^n * n^(n+1/2) / (exp(n) * Pi^(2*n)), where c = -12 / (Pi^(3/2) * exp(5*Pi^2/24)) = -0.275723765924812729... - _Vaclav Kotesovec_, Dec 01 2014, updated Aug 22 2017
%t A247482 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)),{m,1,k}],{k,1,j}],{x,0,j}]==0,koef][[1]]; aa[[j]]=koef/.sol[[1]],{j,2,nmax}]; Flatten[{1,aa}]
%o A247482 (PARI) {a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, 0);
%o A247482 A[#A]=-polcoeff(sum(m=1, #A, prod(k=1, m, 1-1/Ser(A)^(2*k-1))), #A-1)); A[n+1]}
%o A247482 for(n=0, 25, print1(a(n), ", ")) \\ _Vaclav Kotesovec_, Mar 17 2024, after _Paul D. Hanna_
%Y A247482 Cf. A247481 (exponent=1), A249934 (exponent=3), A214692 (exponent=4), A247480 (exponent=5), A214693 (exponent=6), A214694 (exponent=8), A214695 (exponent=10).
%Y A247482 Cf. A214690, A214670.
%K A247482 sign
%O A247482 0,3
%A A247482 _Vaclav Kotesovec_, Dec 01 2014