%I #15 Sep 04 2022 04:09:03
%S 0,3,24,150,840,4410,22176,108108,514800,2406690,11085360,50438388,
%T 227149104,1014058500,4493059200,19777483800,86555576160,376877404530,
%U 1633524354000,7051380128100,30326236340400,129989276677260,555482126422080,2367111334185000,10061252349127200
%N a(n) = (2*n+n^2)*(binomial(2*n,n))/2.
%F From _Amiram Eldar_, Sep 04 2022: (Start)
%F a(n) = A005563(n)*A000984(n)/2.
%F Sum_{n>=1} 1/a(n) = 13/2 - 7*Pi/sqrt(3) + 2*Pi^2/3.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 11/2 - 10*sqrt(5)*log(phi) + 24*log(phi)^2, where phi is the golden ratio (A001622). (End)
%p [seq ((2*n+n^2)*(binomial(2*n,n))/2,n=0..29)];
%t Table[(2n+n^2)Binomial[2*n,n]/2,{n,0,25}] (* _Harvey P. Dale_, Feb 20 2011 *)
%Y Cf. A000984, A001622, A005563.
%K easy,nonn
%O 0,2
%A _Zerinvary Lajos_, May 31 2006