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

Terms

a(0) =1a(1) =2a(2) =7a(3) =27a(4) =107a(5) =429a(6) =1731a(7) =7012a(8) =28478a(9) =115864a(10) =471991a(11) =1924483a(12) =7852083a(13) =32053208a(14) =130893949a(15) =534673600a(16) =2184482707a(17) =8926392419a(18) =36479840422a(19) =149095843951a(20) =609400587426