G.f.: Sum_{n>=0} (1 + x*(1+x)^n)^n / 2^(n+1).

Terms

a(0) =1a(1) =1a(2) =4a(3) =16a(4) =86a(5) =544a(6) =3904a(7) =31328a(8) =276798a(9) =2660564a(10) =27576614a(11) =306051500a(12) =3615559236a(13) =45241980928a(14) =597141146374