a(n) = (1/(4n-1))*C(4n,2n).

Terms

a(0) =-1a(1) =2a(2) =10a(3) =84a(4) =858a(5) =9724a(6) =117572a(7) =1485800a(8) =19389690a(9) =259289580a(10) =3534526380a(11) =48932534040a(12) =686119227300