A247481 - OEIS

%I #15 Mar 28 2024 03:20:41

%S 1,1,-1,-1,-2,-14,-98,-822,-7948,-86590,-1046916,-13892842,-200653570,

%T -3133064534,-52596852266,-944892417438,-18091297436248,

%U -367841660947508,-7916992964642992,-179849204152350892,-4300928485463624458,-108013481381638292266

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

%H Vaclav Kotesovec, <a href="/A247481/b247481.txt">Table of n, a(n) for n = 0..370</a>

%F a(n) ~ c * 12^n * n^n / (exp(n) * Pi^(2*n)), where c = -2*sqrt(6)/(Pi*exp(Pi^2/8)) = -0.45411558500969644... - _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,{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), A249934 (exponent=3), A214692 (exponent=4), A247480 (exponent=5), A214693 (exponent=6), A214694 (exponent=8), A214695 (exponent=10).

%Y Cf. A214690, A214670.

%K sign

%O 0,5

%A _Vaclav Kotesovec_, Dec 01 2014