Cancellation factor in reducing Sum_{k=0...n} n^k/k! to lowest terms.

Terms

a(0) =1a(1) =2a(2) =6a(3) =8a(4) =10a(5) =144a(6) =70a(7) =128a(8) =162a(9) =6400a(10) =22a(11) =6220800a(12) =26a(13) =100352a(14) =182250a(15) =425984a(16) =170a(17) =429981696a(18) =38a(19) =163840000a(20) =13502538a(21) =317194240a(22) =46a(23) =247669456896a(24) =31250a(25) =1417674752a(26) =15943230a(27) =80564191232a(28) =9802a(30) =62