a(n) = floor(exp(13/23)*n!).

Terms

a(0) =1a(1) =3a(2) =10a(3) =42a(4) =211a(5) =1267a(6) =8869a(7) =70956a(8) =638607a(9) =6386072a(10) =70246794a(11) =842961535a(12) =10958499963a(13) =153418999484