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A092580
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Triangle read by rows: T(n,k) is the number of permutations p of [n] in which exactly the first k terms satisfy the up-down property, i.e. p(1)< p(2), p(2)>p(3), p(3)<p(4), ...
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0
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1, 1, 1, 3, 1, 2, 12, 4, 3, 5, 60, 20, 15, 9, 16, 360, 120, 90, 54, 35, 61, 2520, 840, 630, 378, 245, 155, 272, 20160, 6720, 5040, 3024, 1960, 1240, 791, 1385, 181440, 60480, 45360, 27216, 17640, 11160, 7119, 4529, 7936, 1814400, 604800, 453600, 272160
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Row sums are the factorial numbers (A000142). First column is A001710. Second column is A001715. Diagonal is A000111.
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REFERENCES
| E. Deutsch and W. P. Johnson, Create your own permutation statistic, Math. Mag., 77, 130-134, 2004.
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FORMULA
| T(n, k)=n!*[(k+1)*E(k)-E(k+1)]/(k+1)! for k<n and T(n, n)=E(n), where tan(x)+sec(x)=Sum[E(n)x^n/n!, n=0..infinity] (i.e. E(n)=A000111(n)).
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EXAMPLE
| T(4,3)=3 because 1432, 2431, 3421 are the only permutations of [4] in which exactly the first 3 entries satisfy the up-down property.
1; 1,1; 3,1,2; 12,4,3,5; 60,20,15,9,16; 360,120,90,54,35,61;
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CROSSREFS
| Cf. A000111, A001710, A001715, A000142.
Sequence in context: A180771 A109528 A136125 * A004468 A145463 A144107
Adjacent sequences: A092577 A092578 A092579 * A092581 A092582 A092583
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KEYWORD
| nonn,tabl
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu) and Warren P. Johnson (wjohnson(AT)bates.edu), Apr 10 2004
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