a(n) = ceiling(n!/e) with e = A001113 = exp(1).

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =9a(5) =45a(6) =265a(7) =1855a(8) =14833a(9) =133497a(10) =1334961a(11) =14684571a(12) =176214841a(13) =2290792933a(14) =32071101049a(15) =481066515735