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A045531
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Number of sticky functions: endofunctions of [ n ] having a fixed point.
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13
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1, 3, 19, 175, 2101, 31031, 543607, 11012415, 253202761, 6513215599, 185311670611, 5777672071535, 195881901213181, 7174630439858727, 282325794823047151, 11878335717996660991, 532092356706983938321
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..100
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FORMULA
| a(n) = n^n-(n-1)^n.
E.g.f.: (T - x)/(T-T^2), where T=T(x) is Euler's tree function (see A000169).
With interpolated zeros, ceiling(n/2)^ceiling(n/2)-floor(n/2)^ceiling(n/2). - Paul Barry, Jul 13 2005
a(n) = A047969(n,n). - Alford Arnold, May 07 2005.
a(n) = Sum_{i=1,...,n} C(n,i)*(i-1)^(i-1)*(n-i)^(n-i) = Sum_{i=1,...,n} C(n,i)*A000312(i-1)*A000312(n-i). [From Vladimir Shevelev, Sep 30 2010]
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MATHEMATICA
| Table[Sum[Binomial[n, i] (n - 1)^(n - i), {i, 1, n}], {n, 1, 20}]
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PROG
| (MAGMA) [n^n-(n-1)^n: n in [1..20] ]; // Vincenzo Librandi, May 07 2011
(PARI) a(n)=n^n-(n-1)^n \\ Charles R Greathouse IV, May 08, 2011
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CROSSREFS
| Column |a(n, 2)| of A039621. Row sums of triangle A055858.
Cf. A000312, A066274, A066275, A047969.
Sequence in context: A080894 A143768 A083071 * A129481 A156131 A161630
Adjacent sequences: A045528 A045529 A045530 * A045532 A045533 A045534
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KEYWORD
| easy,nonn
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AUTHOR
| Len Smiley (smiley(AT)math.uaa.alaska.edu)
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