a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026780.

Terms

a(0) =1a(1) =1a(2) =4a(3) =6a(4) =20a(5) =34a(6) =105a(7) =191a(8) =563a(9) =1071a(10) =3057a(11) =6007a(12) =16745a(13) =33729a(14) =92332a(15) =189662a(16) =511812a(17) =1068178a(18) =2849404a(19) =6025594a(20) =15921514a(21) =34043204a(22) =89242582a(23) =192621212a(24) =501574732a(25) =1091400122a(26) =2825710822a(27) =6192005260a(28) =15952433940a(29) =35172854946