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A136662
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Number of cycles of the permutations of [1,2,...,n].
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3
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1, 2, 1, 3, 2, 2, 1, 1, 2, 4, 3, 3, 2, 2, 3, 3, 2, 2, 1, 1, 2, 2, 1, 3, 2, 2, 1, 1, 2, 2, 3, 1, 2, 5, 4, 4, 3, 3, 4, 4, 3, 3, 2, 2, 3, 3, 2, 4, 3, 3, 2, 2, 3, 3, 4, 2, 3, 4, 3, 3, 2, 2, 3, 3, 2, 2, 1, 1, 2, 2, 1, 3, 2, 2, 1, 1, 2, 2, 3, 1, 2, 3, 2, 2, 1, 1, 2, 4, 3, 3, 2, 2, 3, 3, 2, 2, 1, 1, 2, 2, 3, 1, 2, 2, 1
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OFFSET
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1,2
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COMMENTS
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The row lengths sequence is A000142(n), n>=1, (factorials).
The permutations of [1,2,...,n] are ordered in the standard way (lexicographic or numerically increasing). E.g., in Maple as permute(n) list for not too large n (around 10).
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LINKS
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FORMULA
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a(n,k) = number of cycles of the k-th permutation of [1,2,...,n] in standard (increasing) order.
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EXAMPLE
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Triangle begins:
[1];
[2,1];
[3,2,2,1,1,2];
[4,3,3,2,2,3,3,2,2,1,1,2,2,1,3,2,2,1,1,2,2,3,1,2];
...
Row n=3: permutations of [1,2,3] in the order [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]. Cycle decomposition: [[[1], [2], [3]], [[1], [2, 3]], [[1, 2], [3]], [[1, 2, 3]], [[1, 3, 2]], [[1, 3], [2]]]. Number of cycles: [3,2,2,1,1,2], the entries of row n=3.
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CROSSREFS
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Row sums (total cycle numbers) A000254.
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KEYWORD
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nonn,easy,tabf
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AUTHOR
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STATUS
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approved
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