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A333706
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Number T(n,k) of permutations p of [n] such that |p(i+k) - p(i)| <> k for i in [n-k]; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
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15
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1, 0, 1, 0, 0, 2, 0, 0, 4, 6, 0, 2, 16, 20, 24, 0, 14, 44, 80, 108, 120, 0, 90, 200, 384, 544, 672, 720, 0, 646, 1288, 2240, 3264, 4128, 4800, 5040, 0, 5242, 9512, 15424, 23040, 28992, 34752, 38880, 40320, 0, 47622, 78652, 123456, 176832, 231936, 280512, 323520, 352800, 362880
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OFFSET
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0,6
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COMMENTS
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T(n,k) is defined for n,k >= 0. The triangle contains only the terms with k<=n. T(n,k) = n! for k>=n.
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LINKS
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EXAMPLE
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Triangle T(n,k) begins:
1;
0, 1;
0, 0, 2;
0, 0, 4, 6;
0, 2, 16, 20, 24;
0, 14, 44, 80, 108, 120;
0, 90, 200, 384, 544, 672, 720;
0, 646, 1288, 2240, 3264, 4128, 4800, 5040;
0, 5242, 9512, 15424, 23040, 28992, 34752, 38880, 40320;
...
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CROSSREFS
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Columns k=0-10 (for n>=k) give: A000007, A002464, A110128, A117574, A189255, A189256, A189271, A360384, A360386, A360462, A360463.
Cf. A000170 (condition is satisfied for all k), A248686 (p(i) at distance k are sorted).
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KEYWORD
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AUTHOR
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STATUS
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approved
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