a(n) = Sum_{k=1..n} (k^2 + k)^(n-k).

Terms

a(0) =1a(1) =3a(2) =11a(3) =57a(4) =397a(5) =3487a(6) =37519a(7) =484437a(8) =7353473a(9) =129104523a(10) =2589967603a(11) =58757627185