a(n) = T(2*n,n), array T as in A055818.

Terms

a(0) =1a(1) =2a(2) =9a(3) =43a(4) =217a(5) =1131a(6) =6017a(7) =32467a(8) =177009a(9) =972691a(10) =5378425a(11) =29889531a(12) =166795977a(13) =934039419a(14) =5246059761a(15) =29540072355a(16) =166708076001a(17) =942651407907