a(n) = Hermite(n,2).

Terms

a(0) =1a(1) =4a(2) =14a(3) =40a(4) =76a(5) =-16a(6) =-824a(7) =-3104a(8) =-880a(9) =46144a(10) =200416a(11) =-121216a(12) =-4894016a(13) =-16666880a(14) =60576896a(15) =708980224a(16) =1018614016a(17) =-18612911104a(18) =-109084520960a(19) =233726715904