a(n) = Hermite(n,3).

Terms

a(0) =1a(1) =6a(2) =34a(3) =180a(4) =876a(5) =3816a(6) =14136a(7) =39024a(8) =36240a(9) =-406944a(10) =-3093984a(11) =-10425024a(12) =5517504a(13) =283305600a(14) =1556378496a(15) =1405714176a(16) =-38257069824a(17) =-274525272576a(18) =-346411261440