a(n) = Sum_{k=0..floor(n/2)} C(n-k,k+2)*2^(n-k-2)*(1/2)^k.

Terms

a(0) =0a(1) =0a(2) =1a(3) =6a(4) =25a(5) =88a(6) =281a(7) =842a(8) =2413a(9) =6692a(10) =18101a(11) =48014a(12) =125393a(13) =323376a(14) =825393a(15) =2088850a(16) =5248853a(17) =13110844a(18) =32584653a(19) =80639446a(20) =198844281a(21) =488813768a(22) =1198491913a(23) =2931934938a(24) =7158830781a(25) =17450923092a(26) =42480107365a(27) =103283553054a(28) =250859152801a(29) =608759955040