a(n) = [x^n] (1 + x*(1+x)^(n-1) )^n.

Terms

a(0) =1a(1) =1a(2) =3a(3) =16a(4) =131a(5) =1306a(6) =15257a(7) =203967a(8) =3047907a(9) =50115310a(10) =896746169a(11) =17308420306a(12) =357767229778