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

Terms

a(0) =1a(1) =2a(2) =6a(3) =21a(4) =85a(5) =382a(6) =1879a(7) =9986a(8) =56818a(9) =343640a(10) =2196596a(11) =14770122a(12) =104063085a(13) =765661874a(14) =5866191429a(15) =46683934520a(16) =385048724001