a(n) = T(2n-1,n), where T is the array in A026148.

Terms

a(0) =1a(1) =4a(2) =20a(3) =111a(4) =616a(5) =3464a(6) =19656a(7) =112370a(8) =646272a(9) =3735324a(10) =21678696a(11) =126256361a(12) =737513400a(13) =4319243760a(14) =25352692620a(15) =149108262264a(16) =878502339712