A000909 a(n) = (2*n)!*(2*n+1)! / n!^2.

1, 12, 720, 100800, 25401600, 10059033600, 5753767219200, 4487938430976000, 4577697199595520000, 5914384781877411840000, 9439358111876349296640000, 18236839872145106841108480000, 41944731705933745734549504000000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

From Karol A. Penson, Jun 04 2009: (Start)

Integral representation of a(n) as n-th moment of a positive function W(x) = (1/4)*BesselK(1,(1/2)*sqrt(x))/Pi on the positive axis: a(n) = Integral_{x=0..oo} x^n*W(x) dx, n >= 0.

This is the solution of the Stieltjes moment problem with the moments a(n).

This solution may not be unique. (End)

References

• E. R. Hansen, A Table of Series and Products, Prentice-Hall, Englewood Cliffs, NJ, 1975, p. 96.

Links

• T. D. Noe, Table of n, a(n) for n = 0..100
• Index to divisibility sequences

Crossrefs

a(n) = 4^n * A079484(n+1).

Programs

Mathematica

Table[(2*n)! (2*n+1)!/n!^2, {n, 0, 15}] (* T. D. Noe, Jun 20 2012 *)

PARI

a(n)=binomial(2*n,n)*(2*n+1)! \\ Charles R Greathouse IV, Jan 12 2012