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

Terms

a(0) =0a(1) =1a(2) =11a(3) =69a(4) =354a(5) =1650a(6) =7293a(7) =31213a(8) =130832a(9) =540702a(10) =2212550a(11) =8989090a(12) =36327810a(13) =146228940a(14) =586823265a(15) =2349424125a(16) =9389012160a(17) =37467344310a(18) =149345215290a(19) =594753416790