A166371 a(n) = (A166351(n))^2 = ((6*n)!/((3*n)!))^2.

1, 14400, 442597478400, 311283409572495360000, 1677789268237349829381980160000, 41145365786974742781838753372569600000000, 3375889771315468222156818412294164248002560000000000

Offset

0,2

Comments

Integral representation as n-th moment of a positive function on a positive half-axis (solution of the Stieltjes moment problem).

In Maple notation: a(n)=int(x^n*((1/6)*BesselK(0,(1/2)*x^(1/6))/(x^(5/6)*Pi)), x=0..infinity), n=0,1... .

This solution is not unique.

Links

G. C. Greubel, Table of n, a(n) for n = 0..50

Formula

G.f.: Sum{n>=0} a(n)*x^n/(n!)^6 = hypergeom([1/6, 1/6, 1/2, 1/2, 5/6, 5/6], [1, 1, 1, 1, 1], 2985984*x).

Asymptotics: a(n) = (2-1/(18*n) + 1/(1296*n^2)+247/(699840*n^3) + O(1/n^4))*(12^n)^6/((exp(n))^6*((1/n)^n)^6), n->infinity.

Mathematica

Table[((6*n)!/(3*n)!)^2, {n, 0, 10}] (* G. C. Greubel, May 10 2016 *)

Prog

(Magma) [(Factorial(6*n)/(Factorial(3*n)))^2: n in [0..20]]; // Vincenzo Librandi, May 11 2016

Crossrefs

Cf. A166351

Sequence in context: A226286 A203729 A144649 * A234487 A234977 A250960

Adjacent sequences: A166368 A166369 A166370 * A166372 A166373 A166374

Keyword

nonn

Author

Karol A. Penson, Oct 13 2009

Status

approved