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%I #27 May 16 2021 12:25:07
%S 0,0,1,11,131,1829,29849,561399,11994247,287420489,7642052309,
%T 223394306387,7123940054219,246181194216957,9165811757198641,
%U 365836296342931439,15584321022199735823,705800730789742512401,33866021217511735389485,1716275655660313589123979
%N a(n) = n^n - (n+1)^(n-1).
%C b(n) = n^n mod (n+1)^(n-1) begins: 0, 0, 1, 11, 6, 533, 13042, 37111, 2428309, ... - _Alex Ratushnyak_, Aug 06 2012
%C a(n) is the number of functions f:{1,2,...,n}->{1,2,...,n} with at least one cycle of length >= 2. - _Geoffrey Critzer_, Jan 11 2013
%C Number of defective parking functions of length n and at least one defect. - _Alois P. Heinz_, Aug 18 2017
%H Alois P. Heinz, <a href="/A101334/b101334.txt">Table of n, a(n) for n = 0..386</a>
%H Peter J. Cameron, Daniel Johannsen, Thomas Prellberg, and Pascal Schweitzer, <a href="https://arxiv.org/abs/0803.0302">Counting Defective Parking Functions</a>, arXiv:0803.0302 [math.CO], 2008.
%F E.g.f.: 1/(1-T(x)) - exp(T(x)) where T(x) is the e.g.f. for A000169. - _Geoffrey Critzer_, Jan 11 2013
%F a(n) = Sum_{k>0} A264902(n,k). - _Alois P. Heinz_, Nov 29 2015
%F a(n) = A000312(n) - A000272(n+1). - _Alois P. Heinz_, Aug 18 2017
%e a(3) = 3^3 - 4^2 = 27-16 = 11.
%t ReplacePart[Table[n^n-(n+1)^(n-1),{n,0,nn}],0,1] (* _Geoffrey Critzer_, Jan 11 2013 *)
%o (PARI) for(x=1,20,print( x^x-(x+1)^(x-1) ))
%o (Python)
%o print([n**n - (n+1)**(n-1) for n in range(33)]) # _Alex Ratushnyak_, Aug 06 2012
%Y Cf. A000272, A000312, A046065, A264902.
%K nonn
%O 0,4
%A _Jorge Coveiro_, Dec 24 2004
%E a(0) prepended by _Alex Ratushnyak_, Aug 06 2012
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