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A092583
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Triangle read by rows: T(n,k) is the number of permutations p of [n] in which the length of the longest initial segment avoiding the 123-pattern is equal to k.
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1, 0, 2, 0, 1, 5, 0, 4, 6, 14, 0, 20, 30, 28, 42, 0, 120, 180, 168, 120, 132, 0, 840, 1260, 1176, 840, 495, 429, 0, 6720, 10080, 9408, 6720, 3960, 2002, 1430, 0, 60480, 90720, 84672, 60480, 35640, 18018, 8008, 4862, 0, 604800, 907200, 846720, 604800, 356400
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Row sums are the factorial numbers (A000142). Diagonal is A000108. T(n,n-1)=binom(2n-2,n-3)=A002694(n-1).
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REFERENCES
| E. Deutsch and W. P. Johnson, Create your own permutation statistic, Math. Mag., 77, 130-134, 2004.
R. Simion and F. W. Schmidt, Restricted permutations, European J. Combin., 6, 383-406, 1985.
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FORMULA
| T(n, k)=n!*binom(2k, k-2)/(k+1)! for k<n; T(n, n)=binom(2n, n)/(n+1).
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EXAMPLE
| T(4,3)=6 because 1324, 1423, 2134, 2314, 3124 and 4123 are the only
permutations of [4] in which the length of the longest initial segment
avoiding the 123 pattern is equal to 3 (i.e. the first three entries do
not contain the 123 pattern but all 4 of them do).
1; 0,2; 0,1,5; 0,4,6,14; 0,20,30,28,42; 0,120,180,168,120,132; 0,840,1260,1176,840,495,429;
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CROSSREFS
| Cf. A000142, A000108, A002694.
Sequence in context: A108263 A134433 A125183 * A193471 A182931 A079134
Adjacent sequences: A092580 A092581 A092582 * A092584 A092585 A092586
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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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