a(n) = floor( exp(13/24)*n! ).

Terms

a(0) =1a(1) =3a(2) =10a(3) =41a(4) =206a(5) =1237a(6) =8663a(7) =69304a(8) =623743a(9) =6237432a(10) =68611760a(11) =823341124a(12) =10703434623a(13) =149848084733