[ exp(5/9)*n! ].

Terms

a(0) =1a(1) =3a(2) =10a(3) =41a(4) =209a(5) =1254a(6) =8784a(7) =70274a(8) =632466a(9) =6324668a(10) =69571349a(11) =834856198a(12) =10853130586a(13) =151943828217