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

Terms

a(0) =1a(1) =0a(2) =3a(3) =0a(4) =6a(5) =6a(6) =10a(7) =30a(8) =15a(9) =90a(10) =36a(11) =210a(12) =133a(13) =420a(14) =456a(15) =784a(16) =1305a(17) =1512a(18) =3205a(19) =3240a(20) =7041a(21) =7590a(22) =14433a(23) =18150a(24) =28801a(25) =42108a(26) =58020a(27) =93132a(28) =120240a(29) =197106