a(n) = A257673(2n,n).

Terms

a(0) =1a(1) =3a(2) =21a(3) =174a(4) =1509a(5) =13473a(6) =122580a(7) =1129999a(8) =10518477a(9) =98644395a(10) =930607321a(11) =8821717743a(12) =83960385396a(13) =801783097911