OFFSET
0,2
FORMULA
From Amiram Eldar, Sep 04 2022: (Start)
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)
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 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Zerinvary Lajos, May 31 2006
STATUS
approved