a(n) = T(2n,n), where T is the array in A026120.

Terms

a(0) =1a(1) =1a(2) =7a(3) =35a(4) =188a(5) =1029a(6) =5730a(7) =32292a(8) =183660a(9) =1052062a(10) =6061247a(11) =35085362a(12) =203888951a(13) =1188784325a(14) =6951007260a(15) =40743883935a(16) =239338600713