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Search: id:A066324
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| A066324 |
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Number of endofunctions on n labeled points constructed from k rooted trees. |
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+0
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| 1, 2, 2, 9, 12, 6, 64, 96, 72, 24, 625, 1000, 900, 480, 120, 7776, 12960, 12960, 8640, 3600, 720, 117649, 201684, 216090, 164640, 88200, 30240, 5040, 2097152, 3670016, 4128768, 3440640, 2150400, 967680, 282240, 40320, 43046721
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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T(n,k) = number of endofunctions with k recurrent elements. - Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu), Jul 06 2006
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REFERENCES
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F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 87, see (2.3.28).
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983, ex. 3.3.32.
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FORMULA
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T(n, k)=k*n^(n-k)*(n-1)!/(n-k)!
E.g.f. (relative to x): A(x, y)=1/(1-y*B(x)) where B(x) is e.g.f. A000169.
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EXAMPLE
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1; 2,2; 9,12,6; 64,96,72,24; 625,1000,900,480,120; ...
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CROSSREFS
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Column 1: A000169. Main diagonal: A000142. T(n, n-1): A062119. Row sums give A000312.
Sequence in context: A143022 A154100 A002880 this_sequence A143146 A039796 A007024
Adjacent sequences: A066321 A066322 A066323 this_sequence A066325 A066326 A066327
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KEYWORD
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nonn,tabl
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net), Dec 14 2001
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