OFFSET
0,2
COMMENTS
Generalization of formula for A172392.
Combinatorial interpretation welcome.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..500
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)
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 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Olivier Gérard, Feb 15 2011
STATUS
approved