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 A119574 #19 Oct 03 2024 06:14:40
%S A119574 4,9,32,125,504,2058,8448,34749,143000,588302,2418624,9934834,
%T A119574 40770352,167152500,684656640,2801810205,11455885080,46801769190,
%U A119574 191055480000,779363066790,3177034283280,12942655253580,52693956656640,214412258531250,871975203591024
%N A119574 a(n) = binomial(2*n,n)*(n+2)^2/(n+1).
%H A119574 Sela Fried, <a href="/A119574/a119574.pdf">On the generating function of A119574</a>, 2024.
%F A119574 Conjectured g.f.: (-1 + 14*x - 36*x^2 + (1 - 4*x)^(3/2))/(2*x*(1 - 4*x)^(3/2)). - _Harvey P. Dale_, Jun 02 2024.
%F A119574 The conjecture is true (see links). - _Sela Fried_, Oct 02 2024.
%F A119574 a(n) = A000108(n)*A000290(n+2). - _Alois P. Heinz_, Oct 02 2024
%p A119574 [seq (binomial(2*n,n)*(n+2)^2/(n+1),n=0..25)];
%t A119574 Table[Binomial[2n,n] (n+2)^2/(n+1),{n,0,30}] (* _Harvey P. Dale_, Jun 02 2024 *)
%Y A119574 Cf. A000108, A000290, A000984, A037965, A110609.
%K A119574 easy,nonn
%O A119574 0,1
%A A119574 _Zerinvary Lajos_, May 31 2006