a(n) = binomial(2*n, n)^2 / (1-2*n).

Terms

a(0) =1a(1) =-4a(2) =-12a(3) =-80a(4) =-700a(5) =-7056a(6) =-77616a(7) =-906048a(8) =-11042460a(9) =-139053200a(10) =-1796567344a(11) =-23696871744a(12) =-317933029232