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

Terms

a(0) =0a(1) =1a(2) =7a(3) =37a(4) =177a(5) =807a(6) =3579a(7) =15591a(8) =67071a(9) =285861a(10) =1209641a(11) =5089517a(12) =21314453a(13) =88918353a(14) =369734553a(15) =1533115953a(16) =6341759073a(17) =26177411943a(18) =107853629643a(19) =443633635743