A119582 a(n) = (n^2+n^3)*(binomial(2*n,n))/2.

0, 2, 36, 360, 2800, 18900, 116424, 672672, 3706560, 19691100, 101615800, 512143632, 2531090016, 12303909800, 58971402000, 279211536000, 1307950928640, 6069709778220, 27933266453400, 127596402318000, 578955421044000, 2611088948908440, 11711414832065520, 52265818258804800

Offset: 0

Author

Zerinvary Lajos, May 31 2006

Keywords

• easy
• nonn

Crossrefs

Cf. A000984, A001622, A011379.

Programs

Maple

[seq ((n^2+n^3)*(binomial(2*n,n))/2,n=0..29)];

Mathematica

a[n_] := (n^2 + n^3) * Binomial[2*n, n]/2; Array[a, 30, 0] (* Amiram Eldar, Sep 04 2022 *)

Formula

From Amiram Eldar, Sep 04 2022: (Start)

a(n) = A011379(n)*A000984(n)/2.

Sum_{n>=1} 1/a(n) = 2*Pi/sqrt(3) - Pi^2/9 - 2.

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)