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

Terms

a(0) =1a(1) =0a(2) =4a(3) =4a(4) =10a(5) =40a(6) =30a(7) =180a(8) =215a(9) =580a(10) =1316a(11) =1960a(12) =5719a(13) =8624a(14) =20420a(15) =39536a(16) =71985a(17) =160584a(18) =276664a(19) =588180a(20) =1099786a(21) =2098480a(22) =4201594a(23) =7665724a(24) =15266640a(25) =28422684a(26) =54252560a(27) =103928876a(28) =193166861a(29) =371012360