a(n) = Sum_{j=0..floor(n/2)} T(n,j), T given by A026736.

Terms

a(0) =1a(1) =1a(2) =3a(3) =4a(4) =12a(5) =18a(6) =51a(7) =81a(8) =220a(9) =361a(10) =952a(11) =1595a(12) =4118a(13) =6999a(14) =17787a(15) =30548a(16) =76696a(17) =132766a(18) =330148a(19) =575054a(20) =1418946a(21) =2483812a(22) =6089912a(23) =10703456a(24) =26104178a(25) =46034722a(26) =111769554a(27) =197665364a(28) =478085534a(29) =847542518