a(n) = Hermite(n,4).

Terms

a(0) =1a(1) =8a(2) =62a(3) =464a(4) =3340a(5) =23008a(6) =150664a(7) =929216a(8) =5324432a(9) =27728000a(10) =125984224a(11) =453313792a(12) =854857408a(13) =-4040671744a(14) =-54551666560a(15) =-323274523648a(16) =-949646192384