OFFSET
0,3
COMMENTS
Combinatorial interpretation welcome.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
D-finite with recurrence n*(n+5)*(n+3)*a(n) -8*(4*n-3)*(2*n-1)*(4*n-1)*a(n-1)=0. - R. J. Mathar, Jul 27 2022
From Vaclav Kotesovec, Feb 17 2024: (Start)
a(n) = 720 * (4*n)! / (n!^2 * (n+3)! * (n+5)!).
a(n) ~ 45 * 2^(8*n + 7/2) / (Pi^(3/2) * n^(19/2)). (End)
MATHEMATICA
CoefficientList[Series[HypergeometricPFQ[{1/4, 1/2, 3/4}, {4, 6}, 256 x], {x, 0, 20}], x]
Table[720 * (4*n)! / (n!^2 * (n+3)! * (n+5)!), {n, 0, 20}] (* Vaclav Kotesovec, Feb 17 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Olivier Gérard, Feb 15 2011
STATUS
approved