%I #14 Feb 17 2024 04:30:28

%S 1,8,140,3360,97020,3171168,113369256,4338459840,175165316040,

%T 7385525026880,322747443674656,14534919841012480,671591162296782000,

%U 31725844951938480000,1527939354203180010000,74847268228930016688000,3722092276301165621547000

%N Expansion of 3F2( (1/2, 3/2, 5/2); (3, 5))(64 x)

%C Generalization of formula for A172392.

%C Combinatorial interpretation welcome.

%H G. C. Greubel, <a href="/A185248/b185248.txt">Table of n, a(n) for n = 0..500</a>

%F 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

%F From _Vaclav Kotesovec_, Feb 17 2024: (Start)

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

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

%t CoefficientList[Series[HypergeometricPFQ[{1/2, 3/2, 5/2}, {3, 5}, 64 x], {x, 0, 20}], x]

%t 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 *)

%Y Cf. A172392.

%K nonn,easy

%O 0,2

%A _Olivier Gérard_, Feb 15 2011