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%I #11 Sep 04 2022 04:09:23
%S 0,2,36,360,2800,18900,116424,672672,3706560,19691100,101615800,
%T 512143632,2531090016,12303909800,58971402000,279211536000,
%U 1307950928640,6069709778220,27933266453400,127596402318000,578955421044000,2611088948908440,11711414832065520,52265818258804800
%N a(n) = (n^2+n^3)*(binomial(2*n,n))/2.
%F From _Amiram Eldar_, Sep 04 2022: (Start)
%F a(n) = A011379(n)*A000984(n)/2.
%F Sum_{n>=1} 1/a(n) = 2*Pi/sqrt(3) - Pi^2/9 - 2.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 2 - 4*sqrt(5)*log(phi) + 12*log(phi)^2, where phi is the golden ratio (A001622). (End)
%p [seq ((n^2+n^3)*(binomial(2*n,n))/2,n=0..29)];
%t a[n_] := (n^2 + n^3) * Binomial[2*n, n]/2; Array[a, 30, 0] (* _Amiram Eldar_, Sep 04 2022 *)
%Y Cf. A000984, A001622, A011379.
%K easy,nonn
%O 0,2
%A _Zerinvary Lajos_, May 31 2006
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