%I #22 Jan 24 2022 03:59:38
%S 0,4,36,240,1400,7560,38808,192192,926640,4375800,20323160,93117024,
%T 421848336,1892909200,8424486000,37228204800,163493866080,
%U 714083503320,3103696272600,13431200244000,57895542104400,248675137991280
%N a(n) = (n + n^2)*(binomial(2*n, n)).
%F From _Amiram Eldar_, Feb 20 2021: (Start)
%F a(n) = A002378(n)*A000984(n).
%F Sum_{n>=1} (-1)^(n+1)/a(n) = -1 + 2*sqrt(5)*log(phi) - 4*log(phi)^2, where log(phi) = A002390. (End)
%F Sum_{n>=1} 1/a(n) = Pi^2/9 - Pi/sqrt(3) + 1. - _Amiram Eldar_, Jan 24 2022
%p [seq ((n+n^2)*(binomial(2*n,n)),n=0..29)];
%t Table[n*(n + 1)*Binomial[2*n, n], {n, 0, 20}] (* _Amiram Eldar_, Feb 20 2021 *)
%o (PARI) a(n) = (n + n^2)*(binomial(2*n, n)); \\ _Michel Marcus_, Feb 20 2021
%Y Cf. A000984, A002378, A002390.
%K easy,nonn
%O 0,2
%A _Zerinvary Lajos_, May 31 2006