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A166750 a(n) = (A001147(n))^3 = 2^(3*n)*GAMMA(n+1/2)^3/Pi^(3/2). 1
1, 1, 27, 3375, 1157625, 843908625, 1123242379875, 2467763508585375, 8328701841475640625, 40918912147169822390625, 280662818417437811777296875, 2599218361363891574869546359375, 31624689802714468791437770554515625, 494135778167413574866215164914306640625 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..160

FORMULA

G.f.: sum(a(n)*x^n/(n!)^3,n=0..infinity) = 4*EllipticK((1/2)*sqrt(2-2*sqrt(1-8*x)))^2/Pi^2, sum(a(n)*x^n/(n!)^4,n=0..infinity)=hypergeom([1/2,1/2,1/2],[1,1,1],8*x).

Asymptotics: a(n) = (2*sqrt(2)/((exp(-1/2))^3*(exp(1/2))^3)-(1/4)*sqrt(2)/((exp(-1/2))^3*(exp(1/2))^3*n)+(1/64)*sqrt(2)/((exp(-1/2))^3*(exp(1/2))^3*n^2)+O(1/n^3))*(2^n)^3/(((1/n)^n)^3*(exp(n))^3), n->infinity.

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*MeijerG([[],[]],[[ -1/2,-1/2,-1/2],[]],x/8)/(8*(Pi)^(3/2)), x=0..infinity), n=0,1... .

This solution is not unique.

a(n) -(2*n-1)^3*a(n-1) +a(n-2) -(2*n-5)^3*a(n-3) =0. - R. J. Mathar, Jul 24 2012

MAPLE

seq((doublefactorial(2*n-1))^3, n=0..15);

MATHEMATICA

Table[((2 n - 1)!!)^3, {n, 0, 30}] (* Vincenzo Librandi, Jul 21 2017 *)

PROG

(MAGMA) DoubleFactorial:=func< n | &*[n..2 by -2] >; [DoubleFactorial((2*n-1))^3: n in [0..20]]; // Vincenzo Librandi, Jul 21 2017

CROSSREFS

Sequence in context: A017559 A069076 A128507 * A195374 A238698 A230169

Adjacent sequences:  A166747 A166748 A166749 * A166751 A166752 A166753

KEYWORD

nonn

AUTHOR

Karol A. Penson, Oct 21 2009

STATUS

approved

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Last modified April 12 22:03 EDT 2021. Contains 342933 sequences. (Running on oeis4.)