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%I #7 Dec 31 2015 00:11:51
%S 1,5,160,9135,750400,80441425,10638828000,1673678753075,
%T 305252823558400,63325918470124125,14724939203560768000,
%U 3793154255510116564375,1072236911373050595840000,329985748809343574149723625,109830285822698899619230720000,39309730439858456963398059166875,15055402080033663459327206195200000,6143747797144623366547686616298003125,2661215654340427415860408455902822400000,1219479030123689259752174147774198563109375,589404548968234611551047396687998740070400000,299658512455145134987556717044427762586006890625,159865819819818837465659104892463315321094144000000
%N E.g.f.: Limit_{N->oo} [ Sum_{n>=0} (N + n)^(5*n) * (x/N^4)^n/n! ] / F(x)^N, where F(x) = Limit_{N->oo} [ Sum_{n>=0} (N + n)^(5*n) * (x/N^4)^n/n! ]^(1/N).
%C The e.g.f. A(x) of this sequence also satisfies:
%C A(x*y) = Limit_{N->oo} [ Sum_{n>=0} (N + n*y)^(5*n) * (x/N^4)^n/n! ] / G(x,y)^N
%C where
%C G(x,y) = Limit_{N->oo} [ Sum_{n>=0} (N + n*y)^(5*n) * (x/N^4)^n/n! ]^(1/N)
%C for all real y.
%e E.g.f.: A(x) = 1 + 5*x + 160*x^2/2! + 9135*x^3/3! + 750400*x^4/4! + 80441425*x^5/5! + 10638828000*x^6/6! + 1673678753075*x^7/7! + 305252823558400*x^8/8! + 63325918470124125*x^9/9! + 14724939203560768000*x^10/10! +...
%e such that
%e A(x) = Limit_{N->oo} [ Sum_{n>=0} (N + n)^(5*n) * (x/N^4)^n/n! ] / F(x)^N
%e where
%e F(x) = Limit_{N->oo} [ Sum_{n>=0} (N + n)^(5*n) * (x/N^4)^n/n! ]^(1/N)
%e and
%e F(x) = 1 + x + 11*x^2/2! + 316*x^3/3! + 15741*x^4/4! + 1140376*x^5/5! + 109350271*x^6/6! + 13100626176*x^7/7! + 1886686497401*x^8/8! + 317762099341696*x^9/9! + 61318533545522451*x^10/10! +...+ A266484(n)*x^n/n! +...
%Y Cf. A266484, A266522, A266523, A266524.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Dec 30 2015
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