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

Terms

a(0) =1a(1) =2a(2) =9a(3) =52a(4) =425a(5) =4236a(6) =49294a(7) =655096a(8) =9731313a(9) =159114880a(10) =2832245911a(11) =54400757016