O15-C080

> restart;
> a:=n->sum(k^n/k!,k=0..infinity);

                                 infinity
                                  -----     n
                                   \       k
                       a := n ->    )     ----
                                   /       k!
                                  -----
                                  k = 0

> res:=[]:for n from 2 to 8 do res:=[op(res),a(n)] od:res;a(12);

  [2 exp(1), 5 exp(1), 15 exp(1), 52 exp(1), 203 exp(1), 877 exp(1),

        4140 exp(1)]


                            4213597 exp(1)

> b[0]:=exp(1):b[1]:=exp(1):for n from 2 to 12 do b[n]:=sum(binomial(n-1,i)*b[i],i=0..n-1) od:
> b[12];

                            4213597 exp(1)

>