a(n) = Sum_{k=0..floor(2*n/5)} binomial(k+2,2) * binomial(k,2*n-5*k).

Terms

a(0) =1a(1) =0a(2) =0a(3) =3a(4) =0a(5) =6a(6) =6a(7) =0a(8) =30a(9) =10a(10) =15a(11) =90a(12) =15a(13) =105a(14) =210a(15) =49a(16) =420a(17) =420a(18) =280a(19) =1260a(20) =801a(21) =1296a(22) =3150a(23) =1755a(24) =4665a(25) =6996a(26) =4950a(27) =13915a(28) =14718a(29) =15840