|
%I #15 Aug 28 2022 08:29:13
%S 0,4,72,720,5600,37800,232848,1345344,7413120,39382200,203231600,
%T 1024287264,5062180032,24607819600,117942804000,558423072000,
%U 2615901857280,12139419556440,55866532906800,255192804636000,1157910842088000,5222177897816880,23422829664131040
%N a(n) = (n^2+n^3)*binomial(2*n,n).
%F From _Amiram Eldar_, Aug 28 2022: (Start)
%F a(n) = (n*(n+1))^2*A000108(n).
%F Sum_{n>=1} 1/a(n) = Pi/sqrt(3) - Pi^2/18 - 1.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 6*log(phi)^2 - 2*sqrt(5)*log(phi) + 1, where phi is the golden ratio (A001622). (End)
%F a(n) = A000984(n)*A011379(n). - _Michel Marcus_, Aug 28 2022
%p [seq ((n^2+n^3)*(binomial(2*n,n)),n=0..29)];
%t Table[(n^2 + n^3) * Binomial[2 n, n], {n, 0, 30}] (* _Wesley Ivan Hurt_, Feb 26 2014 *)
%Y Cf. A000108, A000984, A001622, A011379.
%K easy,nonn
%O 0,2
%A _Zerinvary Lajos_, May 31 2006
|
