a(n) = Sum_{k=0..floor(n/2)} (k+1) * binomial(2*k,2*n-4*k).

Terms

a(0) =1a(1) =0a(2) =2a(3) =2a(4) =3a(5) =18a(6) =7a(7) =60a(8) =65a(9) =144a(10) =356a(11) =410a(12) =1272a(13) =1722a(14) =3743a(15) =7202a(16) =11482a(17) =25566a(18) =40421a(19) =81610a(20) =147169a(21) =259810a(22) =507267a(23) =867792a(24) =1659112a(25) =2961860a(26) =5362592a(27) =9940420a(28) =17583485a(29) =32564548