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

Terms

a(0) =0a(1) =1a(2) =6a(3) =26a(4) =102a(5) =385a(6) =1430a(7) =5278a(8) =19448a(9) =71706a(10) =264860a(11) =980628a(12) =3640210a(13) =13549185a(14) =50565270a(15) =189194550a(16) =709634640a(17) =2667953310a(18) =10052743860a(19) =37957739820a(20) =143606349900a(21) =544321253658