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A065440
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a(n) = (n-1)^n.
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20
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1, 0, 1, 8, 81, 1024, 15625, 279936, 5764801, 134217728, 3486784401, 100000000000, 3138428376721, 106993205379072, 3937376385699289, 155568095557812224, 6568408355712890625, 295147905179352825856, 14063084452067724991009, 708235345355337676357632
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OFFSET
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0,4
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COMMENTS
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a(n) is the number of functions from {1,2,...,n} into {1,2,...,n} that have no fixed points.
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
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LINKS
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FORMULA
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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).
a(n) = Sum_{k=0..n} (-1)^k*binomial(n,k)*n^(n-k). - Robert FERREOL, Mar 28 2017
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MATHEMATICA
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PROG
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(PARI) { for (n=0, 100, write("b065440.txt", n, " ", (n - 1)^n) ) } \\ Harry J. Smith, Oct 19 2009
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CROSSREFS
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Essentially the same as A007778 - note T(x) = -W(-x)).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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