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%I #14 Jun 21 2015 06:36:38
%S 1,2,18,380,14980,969192,94438344,13027041456,2427908305680,
%T 589565047637280,181202801029384992,68849741925654266304,
%U 31716559209036029729856,17426989484519712174940800,11263849940254797456755356800,8462659472067485322490892440320
%N E.g.f.: exp( Sum_{n>=1} x^(2*n) / n^2 ) = Sum_{n>=0} a(n)*x^(2*n)/(2*n)!.
%C Sum_{n>=0} a(n)/(2*n)! = exp(Pi^2/6) = 5.1806683178971...
%H Vaclav Kotesovec, <a href="/A226837/b226837.txt">Table of n, a(n) for n = 0..224</a>
%e E.g.f.: A(x) = 1 + 2*x^2/2! + 18*x^4/4! + 380*x^6/6! + 14980*x^8/8! +...
%e where
%e log(A(x)) = x^2 + x^4/4 + x^6/9 + x^8/16 + x^10/25 + x^12/36 + x^14/49 +...
%t nmax=20; k=2; Table[(CoefficientList[Series[Exp[PolyLog[k,x^k]], {x,0,k*nmax}],x] * Range[0,k*nmax]!)[[k*n-k+1]], {n,1,nmax+1}] (* _Vaclav Kotesovec_, Jun 21 2015 *)
%o (PARI) {a(n)=(2*n)!*polcoeff(exp(sum(m=1,n,(x^m/m)^2)+x*O(x^(2*n))),2*n)}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A258873, A258874.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jun 19 2013
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