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A333310
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Triangle read by rows: T(n,k) is the number of permutations sigma of [n] such that sigma(1) = k and sigma(j)/j > sigma(j+1)/(j+1) for 1 <= j <= n-1.
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2
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1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 1, 2, 0, 1, 2, 2, 1, 3, 0, 1, 3, 5, 2, 3, 5, 0, 1, 3, 6, 5, 3, 4, 8, 0, 1, 4, 8, 12, 8, 5, 9, 13, 0, 1, 4, 12, 20, 18, 8, 11, 13, 21, 0, 1, 5, 18, 29, 42, 21, 22, 19, 27, 38, 0, 1, 5, 23, 44, 69, 48, 33, 30, 33, 38, 64
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OFFSET
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1,13
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COMMENTS
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T(n+1,k+1) is equal to the number of permutations sigma of [n] such that sigma(1) = k and sigma(j)/j >= sigma(j+1)/(j+1) for 1 <= j <= n-1.
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LINKS
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Seiichi Manyama, Rows n = 1..18, flattened
Mathematics.StackExchange, Why are the numbers of two different permutations the same?, Mar 07 2020.
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EXAMPLE
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Triangle begins:
n\k | 1 2 3 4 5 6 7 8 9 10 11 12
-----+--------------------------------------------
1 | 1;
2 | 0, 1;
3 | 0, 1, 1;
4 | 0, 1, 1, 1;
5 | 0, 1, 2, 1, 2;
6 | 0, 1, 2, 2, 1, 3;
7 | 0, 1, 3, 5, 2, 3, 5;
8 | 0, 1, 3, 6, 5, 3, 4, 8;
9 | 0, 1, 4, 8, 12, 8, 5, 9, 13;
10 | 0, 1, 4, 12, 20, 18, 8, 11, 13, 21;
11 | 0, 1, 5, 18, 29, 42, 21, 22, 19, 27, 38;
12 | 0, 1, 5, 23, 44, 69, 48, 33, 30, 33, 38, 64;
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CROSSREFS
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Row sums give A309807.
Cf. A332954.
Sequence in context: A114002 A114004 A306518 * A049986 A218797 A137289
Adjacent sequences: A333307 A333308 A333309 * A333311 A333312 A333313
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KEYWORD
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nonn,tabl
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AUTHOR
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Seiichi Manyama, Mar 14 2020
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STATUS
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approved
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