|
| |
|
|
A000909
|
|
(2n)!(2n+1)! / n!^2.
|
|
2
| |
|
|
1, 12, 720, 100800, 25401600, 10059033600, 5753767219200, 4487938430976000, 4577697199595520000, 5914384781877411840000, 9439358111876349296640000, 18236839872145106841108480000, 41944731705933745734549504000000
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Contribution from Karol A. Penson (penson(AT)lptl.jussieu.fr), 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
| Index to divisibility sequences
|
|
|
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: A171105 A002196 A141421 * A162447 A061025 A042749
Adjacent sequences: A000906 A000907 A000908 * A000910 A000911 A000912
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
