a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(2*k,n-3*k).

Terms

a(0) =1a(1) =0a(2) =0a(3) =3a(4) =8a(5) =5a(6) =15a(7) =84a(8) =168a(9) =228a(10) =765a(11) =2475a(12) =4895a(13) =10010a(14) =30212a(15) =79898a(16) =171080a(17) =411740a(18) =1132404a(19) =2798472a(20) =6470013a(21) =16327650a(22) =42481131a(23) =103773516a(24) =251509071a(25) =638802230a(26) =1618352450a(27) =3979805115a(28) =9869565420a(29) =24973107705