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A075195
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Jablonski table T(n,k) read by antidiagonals: T(n,k) = number of necklaces with n beads of k colors.
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16
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1, 2, 1, 3, 3, 1, 4, 6, 4, 1, 5, 10, 11, 6, 1, 6, 15, 24, 24, 8, 1, 7, 21, 45, 70, 51, 14, 1, 8, 28, 76, 165, 208, 130, 20, 1, 9, 36, 119, 336, 629, 700, 315, 36, 1, 10, 45, 176, 616, 1560, 2635, 2344, 834, 60, 1, 11, 55, 249, 1044, 3367, 7826, 11165, 8230, 2195, 108
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refs;
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history;
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OFFSET
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1,2
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REFERENCES
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F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, pg 86 (2.2.23)
Louis Comtet, Analyse combinatoire, Tome 2, p. 104 #17, P.U.F., 1970.
Jablonski, Theorie des permutations et des arrangements complets, Journal de Liouville, 8 (1892), p 331-49.
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LINKS
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Table of n, a(n) for n=1..65.
Index entries for sequences related to necklaces
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FORMULA
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T(n, k) = (1/n)* Sum_{d divides n}*phi(d)*k^(n/d), where phi = Euler totient function A000010. - Philippe Deléham, Oct 08 2003
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EXAMPLE
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The array T(n,k) for n >= 1, k >= 1 begins:
1 2 3 4 5 ...
1 3 6 10 15 ...
1 4 11 24 45 ...
1 6 24 70 165 ...
1 8 51 208 629 ...
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CROSSREFS
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Columns 1-10: A000012, A000031, A001867, A001868, A001869, A054625-A054629
Rows 1-10: A000027, A000217, A006527, A006528, A054620, A006565, A054621-A054624
Main Diagonal: A056665. A054630 and A054631 are the upper and lower triangles.
Cf. A000010.
Sequence in context: A074909 A135278 A034356 * A126885 A130305 A144400
Adjacent sequences: A075192 A075193 A075194 * A075196 A075197 A075198
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KEYWORD
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nonn,tabl
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AUTHOR
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Christian G. Bower, Sep 07 2002
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EXTENSIONS
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Additional references from Philippe Deléham, Oct 08 2003
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STATUS
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approved
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