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

Terms

a(0) =1a(1) =5a(2) =27a(3) =155a(4) =924a(5) =5643a(6) =35036a(7) =220133a(8) =1395549a(9) =8909120a(10) =57193916a(11) =368849781a(12) =2387828041a(13) =15507998588a(14) =100996781823a(15) =659323123227