OFFSET
0,1
FORMULA
a(n) = Sum_{k=0..n} n!*(k!+1) / (k!*(n-k)!) = Sum_{k=0..n} (P(n, k) + C(n, k)) = Sum_{k=0..n} P(n, k) + 2^n = A007526(n) + A000079(n). - Ross La Haye, Aug 24 2006
EXAMPLE
a(2) = 9 because P(2,0) = 1, P(2,1) = 2, P(2,2) = 2 while C(2,0) = 1, C(2,1) = 2, C(2,2) = 1 and 1 + 1 + 2 + 2 + 2 + 1 = 9.
MATHEMATICA
f[n_] := Sum[n!(k! + 1)/(k!(n - k)!), {k, 0, n}]; Table[ f[n], {n, 0, 20}] (* Robert G. Wilson v, Sep 24 2004 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ross La Haye, Sep 20 2004
STATUS
approved