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

Terms

a(0) =1a(1) =4a(2) =14a(3) =60a(4) =225a(5) =796a(6) =2764a(7) =9304a(8) =30580a(9) =98700a(10) =313422a(11) =981548a(12) =3037473a(13) =9301620a(14) =28222000a(15) =84927760a(16) =253699285a(17) =752863840a(18) =2220831160a(19) =6515581600a(20) =19021079866a(21) =55276625304a(22) =159967084164a(23) =461150383400