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A276837
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Number A(n,k) of permutations of [n] such that for each cycle c the smallest integer interval containing all elements of c has at most k elements; square array A(n,k), n>=0, k>=0, read by antidiagonals.
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11
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1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 2, 3, 1, 0, 1, 1, 2, 6, 5, 1, 0, 1, 1, 2, 6, 12, 8, 1, 0, 1, 1, 2, 6, 24, 25, 13, 1, 0, 1, 1, 2, 6, 24, 60, 57, 21, 1, 0, 1, 1, 2, 6, 24, 120, 150, 124, 34, 1, 0, 1, 1, 2, 6, 24, 120, 360, 399, 268, 55, 1, 0
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OFFSET
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0,13
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COMMENTS
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The sequence of column k satisfies a linear recurrence with constant coefficients of order 2^(k-1) for k>0.
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LINKS
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FORMULA
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A(n,k+1) - A(n,k) = A263757(n,k) for n>0.
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EXAMPLE
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Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
0, 1, 1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 2, 2, 2, 2, 2, 2, ...
0, 1, 3, 6, 6, 6, 6, 6, 6, ...
0, 1, 5, 12, 24, 24, 24, 24, 24, ...
0, 1, 8, 25, 60, 120, 120, 120, 120, ...
0, 1, 13, 57, 150, 360, 720, 720, 720, ...
0, 1, 21, 124, 399, 1050, 2520, 5040, 5040, ...
0, 1, 34, 268, 1145, 3192, 8400, 20160, 40320, ...
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CROSSREFS
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Columns k=0-10 give: A000007, A000012, A000045(n+1), A214663, A276838, A276839, A276840, A276841, A276842, A276843, A276844.
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KEYWORD
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AUTHOR
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STATUS
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approved
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