cp's OEIS Frontend

A266524 E.g.f.: Limit_{N->oo} [ Sum_{n>=0} (N + n)^(4*n) * (x/N^3)^n/n! ] / F(x)^N, where F(x) = Limit_{N->oo} [ Sum_{n>=0} (N + n)^(4*n) * (x/N^3)^n/n! ]^(1/N).

%I A266524 #8 Dec 31 2015 00:12:23
%S A266524 1,4,100,4464,286816,24053120,2488967136,306383969920,43726697867008,
%T A266524 7098711727021056,1291743506952832000,260410631081389420544,
%U A266524 57609344863582419640320,13875489289115958335143936,3614364399291754755286614016,1012444950785630853817442304000,303479487751656117544078504493056,96925825525767333731669511270563840,32859305845564004294368688506268024832,11784943093649049136596829229809817092096,4458038385946160559288726139220234076160000,1773928724624151210275576625473634276174987264,740706616375525604793089813921394696991733186560
%N A266524 E.g.f.: Limit_{N->oo} [ Sum_{n>=0} (N + n)^(4*n) * (x/N^3)^n/n! ] / F(x)^N, where F(x) = Limit_{N->oo} [ Sum_{n>=0} (N + n)^(4*n) * (x/N^3)^n/n! ]^(1/N).
%C A266524 The e.g.f. A(x) of this sequence also satisfies:
%C A266524 A(x*y) = Limit_{N->oo} [ Sum_{n>=0} (N + n*y)^(4*n) * (x/N^3)^n/n! ] / G(x,y)^N
%C A266524 where
%C A266524 G(x,y) = Limit_{N->oo} [ Sum_{n>=0} (N + n*y)^(4*n) * (x/N^3)^n/n! ]^(1/N)
%C A266524 for all real y.
%e A266524 E.g.f.: A(x) = 1 + 4*x + 100*x^2/2! + 4464*x^3/3! + 286816*x^4/4! + 24053120*x^5/5! + 2488967136*x^6/6! + 306383969920*x^7/7! + 43726697867008*x^8/8! + 7098711727021056*x^9/9! + 1291743506952832000*x^10/10! +...
%e A266524 such that
%e A266524 A(x) = Limit_{N->oo} [ Sum_{n>=0} (N + n)^(4*n) * (x/N^3)^n/n! ] / F(x)^N
%e A266524 where
%e A266524 F(x) = Limit_{N->oo} [ Sum_{n>=0} (N + n)^(4*n) * (x/N^3)^n/n! ]^(1/N)
%e A266524 and
%e A266524 F(x) =  1 + x + 9*x^2/2! + 205*x^3/3! + 8033*x^4/4! + 456561*x^5/5! + 34307545*x^6/6! + 3219222301*x^7/7! + 363018204225*x^8/8! + 47866764942721*x^9/9! + 7230829461286121*x^10/10! +...+ A266483(n)*x^n/n! +...
%Y A266524 Cf. A266483, A266522, A266523, A266525.
%K A266524 nonn
%O A266524 0,2
%A A266524 _Paul D. Hanna_, Dec 30 2015