[ exp(4/15)*n! ].

Terms

a(0) =1a(1) =2a(2) =7a(3) =31a(4) =156a(5) =940a(6) =6580a(7) =52642a(8) =473778a(9) =4737780a(10) =52115580a(11) =625386966a(12) =8130030563a(13) =113820427882