a(n) = hypergeom([-1 - n, -n, 1 - n], [2, 3], +2).

Terms

a(0) =1a(1) =1a(2) =-1a(3) =-3a(4) =13a(5) =17a(6) =-241a(7) =121a(8) =5081a(9) =-13327a(10) =-106705a(11) =609589a(12) =1850661a(13) =-23392159a(14) =-6796193a(15) =811545073a(16) =-1688514383a(17) =-25224774367a(18) =123764707231a(19) =650087614573