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

Terms

a(0) =1a(1) =3a(2) =13a(3) =61a(4) =421a(5) =2641a(6) =23521a(7) =203281a(8) =2071441a(9) =22407841a(10) =286403041a(11) =3453468481a(12) =51122111041a(13) =759194916481