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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).
4
1, 4, 100, 4464, 286816, 24053120, 2488967136, 306383969920, 43726697867008, 7098711727021056, 1291743506952832000, 260410631081389420544, 57609344863582419640320, 13875489289115958335143936, 3614364399291754755286614016, 1012444950785630853817442304000, 303479487751656117544078504493056, 96925825525767333731669511270563840, 32859305845564004294368688506268024832, 11784943093649049136596829229809817092096, 4458038385946160559288726139220234076160000, 1773928724624151210275576625473634276174987264, 740706616375525604793089813921394696991733186560
OFFSET
0,2
The e.g.f. A(x) of this sequence also satisfies:
A(x*y) = Limit_{N->oo} [ Sum_{n>=0} (N + n*y)^(4*n) * (x/N^3)^n/n! ] / G(x,y)^N
where
G(x,y) = Limit_{N->oo} [ Sum_{n>=0} (N + n*y)^(4*n) * (x/N^3)^n/n! ]^(1/N)
for all real y.
EXAMPLE
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! +...
such that
A(x) = 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)
and
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! +...
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 30 2015
STATUS
approved

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Last modified September 20 10:44 EDT 2024. Contains 376068 sequences. (Running on oeis4.)