[Maxima] Happy new year.

[Michel Van den Bergh]

> (%i4) sum(n/(3*n+1)/(2*n+1)^2, n, 1, inf)$
> (%i5) closed_form(%), ratsimp;
> (%o5) 
> -(12*sqrt(3)*log(3)-16*sqrt(3)*log(2)-sqrt(3)*%pi^2+4*%pi)/(8*sqrt(3))

I included this very nice example in the demonstration script for levin 
(www.bertold.org/levin).

Michel