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A266485 E.g.f.: Limit_{N->oo} [ Sum_{n>=0} (N + 2*n)^(2*n) * (x/N)^n/n! ]^(1/N). 7
1, 1, 9, 193, 6929, 356001, 24004825, 2012327521, 202156421409, 23701550853313, 3179302948594601, 480443117415138945, 80788534008942735409, 14965275494082095616097, 3028424508967743713615481, 664790043100841638943719201, 157352199248412053285546165825, 39950540529265571984889165180801, 10830877380135708660866040332928841, 3122931260561996112629450841975721537, 954295119605498820582898590882294309201, 308072983118017949662843148184536037793825 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Compare to: Limit_{N->oo} [ Sum_{n>=0} (N + n)^n * x^n/n! ]^(1/N)  =  Sum_{n>=0} (n+1)^(n-1) * x^n/n!.

LINKS

Table of n, a(n) for n=0..21.

EXAMPLE

E.g.f.: A(x) = 1 + x + 9*x^2/2! + 193*x^3/3! + 6929*x^4/4! + 356001*x^5/5! + 24004825*x^6/6! + 2012327521*x^7/7! + 202156421409*x^8/8! + 23701550853313*x^9/9! + 3179302948594601*x^10/10! +...

where A(x) equals the limit, as N -> oo, of the series

[1 + (N+2)^2*(x/N) + (N+4)^4*(x/N)^2/2! + (N+6)^6*(x/N)^3/3! + (N+8)^8*(x/N)^4/4! + (N+10)^10*(x/N)^5/5! + (N+12)^12*(x/N)^6/6! +...]^(1/N).

PROG

(PARI) /* Informal listing of terms 0..30 */

\p300

P(n) = sum(k=0, 32, (n+2*k)^(2*k) * x^k/k! +O(x^31))

Vec( round( serlaplace( subst(P(10^100)^(1/10^100), x, x/10^100) )*1.) )

CROSSREFS

Cf. A266481, A266482, A266483, A266484, A266486, A266487.

Sequence in context: A297517 A116877 A196959 * A279132 A334777 A081020

Adjacent sequences:  A266482 A266483 A266484 * A266486 A266487 A266488

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 30 2015

STATUS

approved

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Last modified May 18 00:59 EDT 2022. Contains 353779 sequences. (Running on oeis4.)