a(n) = T(2n-1,n-1), where T is the array in A026120.

Terms

a(0) =1a(1) =4a(2) =20a(3) =110a(4) =608a(5) =3409a(6) =19304a(7) =110187a(8) =632960a(9) =3654915a(10) =21195716a(11) =123365099a(12) =720240584a(13) =4216176575a(14) =24738092400a(15) =145444454754a(16) =856662911136