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

Terms

a(0) =1a(1) =3a(2) =8a(3) =19a(4) =44a(5) =97a(6) =207a(7) =432a(8) =884a(9) =1777a(10) =3529a(11) =6942a(12) =13547a(13) =26281a(14) =50791a(15) =97942a(16) =188677a(17) =363489a(18) =700953a(19) =1354060a(20) =2621602a(21) =5088832a(22) =9905382a(23) =19335477a(24) =37848971a(25) =74287855a(26) =146173721a(27) =288280956a(28) =569715036a(29) =1127957956