a(n) = 1 + n*binomial(2*n,n) - n^2*(n^2 - 2*n + 3)/2.

Terms

a(0) =1a(1) =2a(2) =7a(3) =34a(4) =193a(5) =1036a(6) =5059a(7) =23094a(8) =101329a(9) =434908a(10) =1843411a(11) =7753582a(12) =32441017a(13) =135195464a(14) =561615643a(15) =2326740526a(16) =9617257185a(17) =39671268460a(18) =163352388259a(19) =671559953358