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%I #15 Feb 17 2024 02:58:15
%S 1,1,12,330,14300,831402,59491432,4971783960,468842704200,
%T 48707547603000,5478624954385440,658555622357831640,
%U 83752779737507765040,11180459218164097480500,1556759031871924444410000,224927463853886185614776400,33579302695870956078753329400,5161336349665341660810732336600
%N Expansion of 3F2( (1/4,1/2,3/4); (4,6) )(256 x)
%C Combinatorial interpretation welcome.
%H Vincenzo Librandi, <a href="/A185247/b185247.txt">Table of n, a(n) for n = 0..200</a>
%F 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
%F From _Vaclav Kotesovec_, Feb 17 2024: (Start)
%F a(n) = 720 * (4*n)! / (n!^2 * (n+3)! * (n+5)!).
%F a(n) ~ 45 * 2^(8*n + 7/2) / (Pi^(3/2) * n^(19/2)). (End)
%t CoefficientList[Series[HypergeometricPFQ[{1/4, 1/2, 3/4}, {4, 6}, 256 x], {x, 0, 20}], x]
%t Table[720 * (4*n)! / (n!^2 * (n+3)! * (n+5)!), {n, 0, 20}] (* _Vaclav Kotesovec_, Feb 17 2024 *)
%K nonn
%O 0,3
%A _Olivier Gérard_, Feb 15 2011
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