a(n) = Sum_{k=0..floor(n/5)} binomial(n+4,5*k+4) * Catalan(k).

Terms

a(0) =1a(1) =5a(2) =15a(3) =35a(4) =70a(5) =127a(6) =220a(7) =385a(8) =715a(9) =1430a(10) =3005a(11) =6400a(12) =13500a(13) =28050a(14) =57800a(15) =119515a(16) =250425a(17) =533525a(18) =1151975a(19) =2504700a(20) =5453176a(21) =11856275a(22) =25748450a(23) =55962300a(24) =121981725a(25) =266968938a(26) =586630515a(27) =1292992795a(28) =2855288480a(29) =6311930460