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%I #12 Aug 10 2021 21:12:00
%S 0,2,23,255,3260,49196,867699,17604595,404662204,10401033404,
%T 295672787215,9211294233871,312080173805324,11423999821072140,
%U 449316582527563515,18896039733447227131,846135945932355895308,40192537618855187742732,2018612071634068368034711
%N a(n) = Sum_{k=0..n} (k^k-k!).
%C a(n) = number of non-injective functions [k]->[k] for 1<=k<=n.
%F a(n) = Sum_{k=0..n} (k^k-k!).
%F a(n) = A062970(n) - A003422(n+1). - _Alois P. Heinz_, Aug 10 2021
%e a(4) = 255 because (1^1-1!)+(2^2-2!)+(3^3-3!)+(4^4-4!) = 255.
%t Accumulate[Table[n^n-n!,{n,20}]] (* _Harvey P. Dale_, Aug 21 2011 *)
%Y Cf. A003422, A062970, A036679.
%K easy,nonn
%O 1,2
%A _Darrell Minor_, Apr 02 2002
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