a(n) = floor(exp(8/19)*n!).

Terms

a(0) =1a(1) =1a(2) =3a(3) =9a(4) =36a(5) =182a(6) =1096a(7) =7678a(8) =61430a(9) =552871a(10) =5528710a(11) =60815817a(12) =729789815a(13) =9487267606a(14) =132821746496