This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A186229 #25 Jul 27 2022 06:20:02
%S A186229 1,14,182,2470,34580,494760,7191690,105793545,1570873850,23500272796,
%T A186229 353724885332,5351515200668,81313973049064,1240116577389200,
%U A186229 18973783634054760,291115203548084370,4477664537437798980,69023046543088792440,1066084706728274263800,16495237916832025427160,255635559046076610807120
%N A186229 Expansion of (2F1( (-(1/2), 1/6); (-2/3))( 16 x) -1)/(2*x).
%C A186229 Combinatorial interpretation welcome.
%C A186229 Probably a class of paths (Cf. A135404, A000888)
%H A186229 Vincenzo Librandi, <a href="/A186229/b186229.txt">Table of n, a(n) for n = 0..200</a>
%F A186229 D-finite with recurrence (n+1)*(3n-2)*a(n) = 4*(6n+1)*(2n-1)*a(n-1). - _R. J. Mathar_, Jul 11 2012
%F A186229 a(n) ~ 3*GAMMA(2/3)*2^(1/3) * 16^n/(Pi*n^(2/3)). - _Vaclav Kotesovec_, Aug 13 2013
%F A186229 a(n) = -2^(1/3+4*n)*(-4/3)!*(-1/2+n)!*(1/6+n)!/(Pi*(-2/3+n)!*(1+n)!). - _Benedict W. J. Irwin_, Jul 12 2016
%t A186229 CoefficientList[Series[(HypergeometricPFQ[{-(1/2), 1/6}, {-(2/3)}, 16 x] - 1)/(2 x), {x, 0, 20}], x]
%t A186229 FullSimplify[Table[-((2^(1/3 + 4 n) (-(4/3))! (-(1/2) + n)! (1/6 + n)!)/(Pi (-(2/3) + n)! (1 + n)!)), {n, 0, 20}]] (* _Benedict W. J. Irwin_, Jul 12 2016 *)
%K A186229 nonn,easy
%O A186229 0,2
%A A186229 _Olivier Gérard_, Feb 15 2011