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 A186264 #20 Feb 08 2021 07:47:21
%S A186264 1,3,15,98,756,6534,61347,613470,6447012,70526404,797490876,
%T A186264 9271926888,110380082000,1341117996300,16586474042475,208360804638150,
%U A186264 2653858669601700,34220809160653500,446174168961282300,5875592302944678600,78078028942687784400
%N A186264 Expansion of 3F2( 1, 3/2, 3/2; 3, 4;16 x).
%C A186264 Combinatorial interpretation welcome.
%H A186264 Vincenzo Librandi, <a href="/A186264/b186264.txt">Table of n, a(n) for n = 0..200</a>
%F A186264 G.f. is equivalent to -3*( 1+2*x -2F1(-1/2,-1/2;2;16*x) ) /(4*x^2).
%F A186264 a(n) = 3/((n+3)*(n+2)^2)*(2*n+2)!^2/(n+1)!^4 = 3/(n+3)* Catalan(n+1)^2. - _Peter Bala_, Mar 28 2018
%F A186264 D-finite with recurrence (n+3)*(n+2)*a(n) -4*(2*n+1)^2*a(n-1)=0. - _R. J. Mathar_, Feb 08 2021
%p A186264 seq(3/((n+3)*(n+2)^2)*binomial(2*n+2,n+1)^2, n = 0..20); # _Peter Bala_, Mar 28 2018
%t A186264 CoefficientList[Series[HypergeometricPFQ[{1, 3/2, 3/2}, {3, 4}, 16*x], {x, 0, 20}],
%t A186264 x]
%Y A186264 Cf. A186262, A000108, A001246.
%K A186264 nonn,easy
%O A186264 0,2
%A A186264 _Olivier Gérard_, Feb 16 2011