A185248 Expansion of 3F2( (1/2, 3/2, 5/2); (3, 5))(64 x).

1, 8, 140, 3360, 97020, 3171168, 113369256, 4338459840, 175165316040, 7385525026880, 322747443674656, 14534919841012480, 671591162296782000, 31725844951938480000, 1527939354203180010000, 74847268228930016688000, 3722092276301165621547000

Offset: 0

Author

Olivier Gérard, Feb 15 2011

Keywords

• nonn
• easy

Comments

Generalization of formula for A172392.

Combinatorial interpretation welcome.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A172392.

Programs

Mathematica

CoefficientList[Series[HypergeometricPFQ[{1/2, 3/2, 5/2}, {3, 5}, 64 x], {x, 0, 20}], x]
Table[16 * (2*n+3) * (2*n+1)^2 * (2*n)!^3 / (n!^4 * (n+2)! * (n+4)!), {n, 0, 20}] (* Vaclav Kotesovec, Feb 17 2024 *)

Formula

D-finite with recurrence +n*(n+4)*(n+2)*a(n) -8*(2*n+3)*(2*n+1)*(2*n-1)*a(n-1)=0. - R. J. Mathar, Jul 27 2022

From Vaclav Kotesovec, Feb 17 2024: (Start)

a(n) = 16 * (2*n+3) * (2*n+1)^2 * (2*n)!^3 / (n!^4 * (n+2)! * (n+4)!).

a(n) ~ 2^(6*n + 7) / (Pi^(3/2) * n^(9/2)). (End)