A266525 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).

1, 5, 160, 9135, 750400, 80441425, 10638828000, 1673678753075, 305252823558400, 63325918470124125, 14724939203560768000, 3793154255510116564375, 1072236911373050595840000, 329985748809343574149723625, 109830285822698899619230720000, 39309730439858456963398059166875, 15055402080033663459327206195200000, 6143747797144623366547686616298003125, 2661215654340427415860408455902822400000, 1219479030123689259752174147774198563109375, 589404548968234611551047396687998740070400000, 299658512455145134987556717044427762586006890625, 159865819819818837465659104892463315321094144000000

Offset

0,2

Comments

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

A(x*y) = Limit_{N->oo} [ Sum_{n>=0} (N + n*y)^(5*n) * (x/N^4)^n/n! ] / G(x,y)^N

where

G(x,y) = Limit_{N->oo} [ Sum_{n>=0} (N + n*y)^(5*n) * (x/N^4)^n/n! ]^(1/N)

for all real y.

Links

Table of n, a(n) for n=0..22.

Example

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! +...
such that
A(x) = 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)
and
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! +...

Crossrefs

Cf. A266484, A266522, A266523, A266524.

Sequence in context: A088694 A208583 A197310 * A085330 A222628 A287032

Adjacent sequences: A266522 A266523 A266524 * A266526 A266527 A266528

Keyword

nonn

Author

Paul D. Hanna, Dec 30 2015

Status

approved