a(n) = 2*a(n-1)+(n-2)*a(n-2)-(n-1)*a(n-3) with initial terms (1,2,4).

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =18a(5) =44a(6) =120a(7) =352a(8) =1116a(9) =3736a(10) =13232a(11) =48928a(12) =189080a(13) =757584a(14) =3148064a(15) =13497600a(16) =59704336a(17) =271503648a(18) =1268817472a(19) =6078518912a(20) =29837183008a(21) =149789875904a(22) =768674514816