a(n) = Sum_{k=0..floor(n/2)} binomial(k+3,3) * binomial(2*k,2*n-4*k).

Terms

a(0) =1a(1) =0a(2) =4a(3) =4a(4) =10a(5) =60a(6) =30a(7) =300a(8) =335a(9) =1000a(10) =2506a(11) =3500a(12) =11879a(13) =17304a(14) =44220a(15) =88592a(16) =161865a(17) =385704a(18) =660964a(19) =1475100a(20) =2807956a(21) =5459860a(22) =11313094a(23) =20816004a(24) =42774780a(25) =80798128a(26) =157292750a(27) =307887904a(28) =579776799a(29) =1138007940