OFFSET
0,2
FORMULA
From Amiram Eldar, Aug 28 2022: (Start)
a(n) = (n*(n+1))^2*A000108(n).
Sum_{n>=1} 1/a(n) = Pi/sqrt(3) - Pi^2/18 - 1.
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)
MAPLE
[seq ((n^2+n^3)*(binomial(2*n, n)), n=0..29)];
MATHEMATICA
Table[(n^2 + n^3) * Binomial[2 n, n], {n, 0, 30}] (* Wesley Ivan Hurt, Feb 26 2014 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Zerinvary Lajos, May 31 2006
STATUS
approved