A002627 and A002467

[vdmcc]

A002627 : a(n)=n!*Sum(1/k!,k=1..n)  can also be
written as   -Gamma[1+n]+E Gamma[1+n,1] which is no big deal,

but is it evident that

   A002467 :  a(n)=(n-1)(a(n-1)+a(n-2)); or a(1)=1, a(n)=n*a(n-1)-(-1)^n; or
a(0) = 0,
                        a(n) =  [n!(e-1)/e + 1/2] for n > 0.

is also  Table[  (n)! Sum[(-1)^(w+1)/w!   ,{w,n}],{n,24}]
or alternatively  Gamma[1 + n] - Gamma[1 + n, -1]/E

to me, not simply so.

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