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

Terms

a(0) =1a(1) =3a(2) =16a(3) =84a(4) =458a(5) =2541a(6) =14286a(7) =81103a(8) =463913a(9) =2669576a(10) =15437366a(11) =89633392a(12) =522223740a(13) =3051529665a(14) =17876415654a(15) =104955553899a(16) =617415739622