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

Terms

a(0) =0a(1) =1a(2) =5a(3) =25a(4) =129a(5) =681a(6) =3653a(7) =19825a(8) =108545a(9) =598417a(10) =3317445a(11) =18474633a(12) =103274625a(13) =579168825a(14) =3256957317a(15) =18359266785a(16) =103706427393a(17) =586889743905