G.f.: ((1-q)^2+(1+q)*sqrt(1-6*q+q^2))/2.

Terms

a(0) =1a(1) =-2a(2) =-3a(3) =-8a(4) =-28a(5) =-112a(6) =-484a(7) =-2200a(8) =-10364a(9) =-50144a(10) =-247684a(11) =-1243816a(12) =-6331164a(13) =-32591184a(14) =-169376484a(15) =-887465784a(16) =-4682990076a(17) =-24864759744a(18) =-132745182724a(19) =-712136879944