a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(n-1,n-3*k).

Terms

a(0) =1a(1) =0a(2) =0a(3) =3a(4) =12a(5) =30a(6) =75a(7) =231a(8) =756a(9) =2352a(10) =7110a(11) =21780a(12) =67947a(13) =212784a(14) =664755a(15) =2077803a(16) =6515460a(17) =20486088a(18) =64501536a(19) =203289417a(20) =641479482a(21) =2026745010a(22) =6410455128a(23) =20294491140a(24) =64303461387a(25) =203910988680a(26) =647103880800