a(n) = T(2n,n), where T is the array in A026323.

Terms

a(0) =1a(1) =2a(2) =10a(3) =50a(4) =266a(5) =1452a(6) =8073a(7) =45460a(8) =258434a(9) =1479986a(10) =8525205a(11) =49342636a(12) =286721450a(13) =1671668520a(14) =9774222930a(15) =57291319170a(16) =336537958394