a(n) = n! * Sum_{k=1..n} floor(n/k)/k!.

Terms

a(0) =1a(1) =5a(2) =22a(3) =125a(4) =746a(5) =5677a(6) =44780a(7) =420401a(8) =4206970a(9) =47543141a(10) =562891352a(11) =7573655905a(12) =104684547566