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%I #9 Jun 21 2015 06:36:58
%S 1,24,22680,115684800,1906520616000,80659993905114624,
%T 7746053047976698430976,1560262733456599283808153600,
%U 616206470499428864091871431168000,445310234257659546728524999957770240000,549601486893233034601458951894087488929628160
%N E.g.f.: exp( Sum_{n>=1} x^(4*n) / n^4 ) = Sum_{n>=0} a(n) * x^(4*n) / (4*n)!.
%C Sum_{n>=0} a(n)/(4*n)! = exp( Pi^4/90 ) = 2.95152868285335573659431343...
%H Vaclav Kotesovec, <a href="/A258874/b258874.txt">Table of n, a(n) for n = 0..112</a>
%e E.g.f.: A(x) = 1 + 24*x^4/4! + 22680*x^8/8! + 115684800*x^12/12! + 1906520616000*x^16/16! +...
%e where
%e log(A(x)) = x^4 + x^8/2^4 + x^12/3^4 + x^16/4^4 + x^20/5^4 + x^24/6^4 +...
%e or,
%e log(A(x)) = 24*x^4/4! + 2520*x^8/8! + 5913600*x^12/12! + 81729648000*x^16/16! + 3892643213082624*x^20/20! +...
%t nmax=20; k=4; 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) = (4*n)!*polcoeff( exp(sum(m=1, n, (x^m/m)^4)+x*O(x^(4*n))), 4*n)}
%o for(n=0, 20, print1(a(n), ", "))
%Y Cf. A226837, A258873.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jun 13 2015
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