G.f.: x * Product_{k>=1} (1 + a(k)*(-x)^k)^((-1)^k).

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =8a(5) =18a(6) =44a(7) =104a(8) =246a(9) =620a(10) =1600a(11) =4082a(12) =10436a(13) =27360a(14) =73046a(15) =193296a(16) =509984a(17) =1371214a(18) =3727792a(19) =10065872a(20) =27145058a(21) =74142688a(22) =204005440a(23) =558475342a(24) =1527058912a(25) =4213709856a(26) =11694035010a(27) =32331790700a(28) =89266126856a(29) =248240818282