a(n) = (1/(n+1)) * Sum_{k=0..n} k^3 * (k+1) * binomial(2*n-k,n-k).

Terms

a(0) =0a(1) =1a(2) =10a(3) =56a(4) =258a(5) =1089a(6) =4394a(7) =17290a(8) =67048a(9) =257754a(10) =985796a(11) =3759074a(12) =14311750a(13) =54452385a(14) =207163530a(15) =788414010a(16) =3002300400a(17) =11441617950a(18) =43641721260a(19) =166619689080a(20) =636761192964