a(n) = T(2n,n), where T is the array in A055830.

Terms

a(0) =1a(1) =1a(2) =4a(3) =18a(4) =85a(5) =413a(6) =2044a(7) =10248a(8) =51876a(9) =264550a(10) =1357070a(11) =6994780a(12) =36196706a(13) =187938842a(14) =978599560a(15) =5108177816a(16) =26721644973a(17) =140050505085a(18) =735254208670