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A000909 a(n) = (2n)!(2n+1)! / n!^2. 3
1, 12, 720, 100800, 25401600, 10059033600, 5753767219200, 4487938430976000, 4577697199595520000, 5914384781877411840000, 9439358111876349296640000, 18236839872145106841108480000, 41944731705933745734549504000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

Integral representation of a(n) as n-th moment of a positive function W(x) on the positive axis, in Maple notation: a(n)=int(x^n*W(x),x=0..infinity) = int(x^n*(1/4)*BesselK(1,(1/2)*sqrt(x))/Pi,x=0..infinity), n=0,1,... .

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

MATHEMATICA

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

PROG

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

CROSSREFS

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

Sequence in context: A262383 A002196 A141421 * A162447 A061025 A042749

Adjacent sequences:  A000906 A000907 A000908 * A000910 A000911 A000912

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified September 30 18:12 EDT 2020. Contains 337440 sequences. (Running on oeis4.)