A228080 (5*n+2)!/(2*(n!)^5), n >= 0.

1, 2520, 7484400, 22870848000, 70579794285000, 218799620836917120, 679953587124305894400, 2116187746296592370688000, 6592431144164903462359935000, 20550499897066845200729434200000, 64091912654977017603465324370118400, 199956261330234671205699024876891648000

Offset: 0

Author

Karol A. Penson, Aug 09 2013

Keywords

• nonn

Comments

Although limit( a(n)^(1/n), n=infinity ) = 5^5, apparently this sequence is not a Hausdorff moment sequence of any positive function on (0,5^5).

Crossrefs

Cf. A002544.

Programs

Maple

seq((5*n+2)!/(2*(n!)^5), n=0..11).

Mathematica

Table[(5n+2)!/(2(n!)^5),{n,0,15}] (* Harvey P. Dale, Aug 04 2019 *)

Formula

In Maple notation:

O.g.f. : hypergeom([3/5, 4/5, 6/5, 7/5], [1, 1, 1], 5^5*z);

E.g.f. : hypergeom([3/5, 4/5, 6/5, 7/5], [1, 1, 1, 1], 5^5*z);

Asymptotics: a(n) -> (25*n^2+5*n-2)*(5^(5*n+1/2))* n^(-2)/(8*Pi^2), for n -> infinity.

D-finite with recurrence (n^4)*a(n) -5*(5*n+1)*(5*n+2)*(5*n-2)*(5*n-1)*a(n-1)=0. - R. J. Mathar, Jul 27 2022