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

Terms

a(0) =1a(1) =3a(2) =16a(3) =84a(4) =459a(5) =2552a(6) =14377a(7) =81768a(8) =468468a(9) =2699596a(10) =15630384a(11) =90853864a(12) =529850815a(13) =3098789865a(14) =18167417169a(15) =106738859744a(16) =628304239266