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

Terms

a(0) =1a(1) =1a(2) =5a(3) =22a(4) =101a(5) =476a(6) =2282a(7) =11075a(8) =54245a(9) =267592a(10) =1327580a(11) =6617128a(12) =33110090a(13) =166215895a(14) =836761343a(15) =4222640822a(16) =21354409445a(17) =108193910000a(18) =549084400088