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%I #8 Jun 02 2024 13:30:28
%S 4,9,32,125,504,2058,8448,34749,143000,588302,2418624,9934834,
%T 40770352,167152500,684656640,2801810205,11455885080,46801769190,
%U 191055480000,779363066790,3177034283280,12942655253580,52693956656640
%N a(n) = binomial(2*n,n)*(n+2)^2/(n+1).
%C Conjectured generating function: -((-1 + Sqrt[1 - 4 x] + 14 x - 4 Sqrt[1 - 4 x] x - 36 x^2)/(
%C 2 Sqrt[1 - 4 x] x (-1 + 4 x))). - _Harvey P. Dale_, Jun 02 2024
%p [seq (binomial(2*n,n)*(n+2)^2/(n+1),n=0..25)];
%t Table[Binomial[2n,n] (n+2)^2/(n+1),{n,0,30}] (* _Harvey P. Dale_, Jun 02 2024 *)
%Y Cf. A000984.
%K easy,nonn
%O 0,1
%A _Zerinvary Lajos_, May 31 2006
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