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%I #46 Dec 31 2021 15:41:44
%S 1,0,1,8,81,1024,15625,279936,5764801,134217728,3486784401,
%T 100000000000,3138428376721,106993205379072,3937376385699289,
%U 155568095557812224,6568408355712890625,295147905179352825856,14063084452067724991009,708235345355337676357632
%N a(n) = (n-1)^n.
%C a(n) is the number of functions from {1,2,...,n} into {1,2,...,n} that have no fixed points.
%C The probability that a random function from {1,2,...,n} into {1,2,...,n} has no fixed point is equal to a(n)/n^n; it tends to 1/e when n tends to infinity. - _Robert FERREOL_, Mar 29 2017
%H Harry J. Smith, <a href="/A065440/b065440.txt">Table of n, a(n) for n = 0..100</a>
%H Mustafa Obaid et al., <a href="http://arxiv.org/abs/1307.7573">The number of complete exceptional sequences for a Dynkin algebra</a>, arXiv preprint arXiv:1307.7573 [math.RT], 2013.
%F a(n) = A007778(n-1).
%F E.g.f.: x/(T(x)*(1-T(x))) (where T(x) is Euler's tree function, the E.g.f. for n^(n-1)) (see A000169).
%F a(n) = Sum_{k=0..n} (-1)^k*binomial(n,k)*n^(n-k). - _Robert FERREOL_, Mar 28 2017
%t Table[(n-1)^n,{n,0,20}] (* _Harvey P. Dale_, Jan 03 2015 *)
%o (PARI) { for (n=0, 100, write("b065440.txt", n, " ", (n - 1)^n) ) } \\ _Harry J. Smith_, Oct 19 2009
%Y Essentially the same as A007778 - note T(x) = -W(-x)).
%Y Column k=0 of A055134.
%Y Row sums of A350452.
%Y Cf. A284458.
%K nonn,easy
%O 0,4
%A _Len Smiley_, Nov 17 2001
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