The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A172492 a(n) = (n!)^2*(n+1)!. 3

%I #11 Apr 22 2024 07:34:38

%S 1,2,24,864,69120,10368000,2612736000,1024192512000,589934886912000,

%T 477847258398720000,525631984238592000000,763217641114435584000000,

%U 1428743424166223413248000000,3380406941577284595744768000000

%N a(n) = (n!)^2*(n+1)!.

%C Asymptotics: a(n)->(1/16)*Pi^(3/2)*sqrt(2)*(32*n^2+40*n+9)*exp(-3*n)*(n)^(1/2+3*n), n->infinity.

%F Generating function of hypergeometric type, in Maple notation: sum(a(n)*x^n/(n!)^3, n=0..infinity)=1/(1-x)^2.

%F 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*MeijerG([[],[]],[[0,0,1],[]],x),x=0..infinity), n=0,1... .

%F The MeijerG function above cannot be represented by any other known special function.

%F This solution of the Stieltjes moment problem is not unique.

%o (Python)

%o from math import factorial

%o def A172492(n): return factorial(n)**3*(n+1) # _Chai Wah Wu_, Apr 22 2024

%K nonn

%O 0,2

%A _Karol A. Penson_, Feb 05 2010

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 26 05:37 EDT 2024. Contains 372807 sequences. (Running on oeis4.)