A266523 E.g.f.: Limit_{N->oo} [ Sum_{n>=0} (N + n)^(3*n) * (x/N^2)^n/n! ] / F(x)^N, where F(x) = Limit_{N->oo} [ Sum_{n>=0} (N + n)^(3*n) * (x/N^2)^n/n! ]^(1/N).

1, 3, 54, 1737, 80460, 4866075, 363195144, 32252007249, 3320837109648, 388974074329395, 51071746190248800, 7429243977263853657, 1185973466659967427264, 206128694834273499148107, 38747184998101320725389440, 7832602778214436587234950625, 1694328566956587966290832896256, 390523839870137752804243701312099, 95545779571238219801892087161845248, 24730355203857044123269648640967753705, 6751503716745494652518864431722119040000, 1938877409334089151858199776112230794503803

Offset: 0

Author

Paul D. Hanna, Dec 30 2015

Keywords

• nonn

Comments

The e.g.f. A(x) of this sequence also satisfies:

A(x*y) = Limit_{N->oo} [ Sum_{n>=0} (N + n*y)^(3*n) * (x/N^2)^n/n! ] / G(x,y)^N

where

G(x,y) = Limit_{N->oo} [ Sum_{n>=0} (N + n*y)^(3*n) * (x/N^2)^n/n! ]^(1/N)

for all real y.

Examples

			E.g.f.: A(x) = 1 + 3*x + 54*x^2/2! + 1737*x^3/3! + 80460*x^4/4! + 4866075*x^5/5! + 363195144*x^6/6! + 32252007249*x^7/7! + 3320837109648*x^8/8! + 388974074329395*x^9/9! + 51071746190248800*x^10/10! +...
such that
A(x) = Limit_{N->oo} [ Sum_{n>=0} (N + n)^(3*n) * (x/N^2)^n/n! ] / F(x)^N
where
F(x) = Limit_{N->oo} [ Sum_{n>=0} (N + n)^(3*n) * (x/N^2)^n/n! ]^(1/N)
and
F(x) = 1 + x + 7*x^2/2! + 118*x^3/3! + 3373*x^4/4! + 139096*x^5/5! + 7565779*x^6/6! + 513277024*x^7/7! + 41820455065*x^8/8! + 3982842285184*x^9/9! + 434457816912991*x^10/10! +...+ A266482(n)*x^n/n! +...
		

Crossrefs

Cf. A266482, A266522, A266524, A266525.