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

Terms

a(0) =1a(1) =1a(2) =7a(3) =43a(4) =371a(5) =3926a(6) =47622a(7) =654151a(8) =9999523a(9) =167557174a(10) =3046387103a(11) =59616689595