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A166334 a(n) = (3*n)!/(2^n*n!). 3
1, 3, 90, 7560, 1247400, 340540200, 138940401600, 79196028912000, 60109785944208000, 58607041295602800000, 71383376298044210400000, 106218463931489785075200000, 189599958117709266359232000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Integral representation as n-th moment of a positive function on a positive halfaxis (solution of the Stieltjes moment problem), in Maple notation: a(n) = int(x^n*(1/3)*sqrt(2)*BesselK(1/3,(2/9)*sqrt(6*x))/(sqrt(x)*Pi), x=0..infinity), n=0,1... .

This solution is unique.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..100

FORMULA

G.f.: sum(a(n)*x^(n)/(n!)^2,n=0..infinity)=hypergeom([1/3, 2/3], [1], (27/2)*x).

Asymptotics: a(n)=(sqrt(3)-(1/18)*sqrt(3)/n+(1/648)*sqrt(3)/n^2 +(463/174960)*sqrt(3)/n^3+O(1/n^4))*(3^n)^3/(((1/n)^n)^2*(exp(n))^2*2^n), n->infinity.

E.g.f.: (of aerated sequence) 2*sqrt(2)*cos(arcsin((3*sqrt(6)x/4)/3))/sqrt(8-27x^2). - Paul Barry, Jul 27 2010

2*a(n) = 3*(3*n-1)*(3*n-2)*a(n-1). - R. J. Mathar, Jul 24 2012

MATHEMATICA

Table[(3*n)!/(2^n*n!), {n, 0, 10}] (* G. C. Greubel, May 09 2016 *)

PROG

(Magma) [Factorial(3*n)/(2^n*Factorial(n)): n in [0..20]]; // Vincenzo Librandi, May 10 2016

CROSSREFS

Sequence in context: A013298 A013302 A013303 * A209495 A168408 A132556

Adjacent sequences:  A166331 A166332 A166333 * A166335 A166336 A166337

KEYWORD

nonn

AUTHOR

Karol A. Penson, Oct 12 2009

STATUS

approved

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Last modified September 24 21:38 EDT 2022. Contains 356949 sequences. (Running on oeis4.)