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

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =9a(5) =23a(6) =62a(7) =179a(8) =549a(9) =1773a(10) =6003a(11) =21233a(12) =78187a(13) =298894a(14) =1183387a(15) =4842221a(16) =20438964a(17) =88849325a(18) =397183838a(19) =1823456223a(20) =8587051052a(21) =41434641992a(22) =204654311282