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A066274
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Number of endofunctions of [n] such that 1 is not a fixed point.
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8
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0, 2, 18, 192, 2500, 38880, 705894, 14680064, 344373768, 9000000000, 259374246010, 8173092077568, 279577021469772, 10318292052303872, 408700964355468750, 17293822569102704640, 778579070010669895696, 37160496515557841043456, 1874292305362402347591138
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OFFSET
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1,2
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COMMENTS
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a(n) is the number of functional digraphs that are not a solitary rooted tree. - Geoffrey Critzer, Aug 31 2013
For n > 1 a(n) is the number of numbers with n digits in base n. - Gionata Neri, Feb 18 2016
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LINKS
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FORMULA
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a(n) = n^n - n^(n-1).
E.g.f.: T^2/(1-T), where T=T(x) is Euler's tree function (see A000169).
For n > 1 a(n)=1/(Integral_{x=n..infinity} 1/x^n dx). - Francesco Daddi, Aug 01 2011
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EXAMPLE
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a(2)=2: [1->2,2->1], [1->2,2->2].
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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