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A008304
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Triangle read by rows: T(n,k) (n>=1; 1<=k<=n) is the number of permutations of [n] in which the longest run has length k.
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9
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1, 1, 1, 1, 4, 1, 1, 16, 6, 1, 1, 69, 41, 8, 1, 1, 348, 293, 67, 10, 1, 1, 2016, 2309, 602, 99, 12, 1, 1, 13357, 19975, 5811, 1024, 137, 14, 1, 1, 99376, 189524, 60875, 11304, 1602, 181, 16, 1, 1, 822040, 1960041, 690729, 133669, 19710, 2360, 231, 18, 1, 1, 7477161
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Row n has n terms.
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REFERENCES
| F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 261, Table 7.4.1.
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LINKS
| D. W. Wilson, Extended tables for A008304 and A064315
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EXAMPLE
| 1; 1,1; 1,4,1; 1,16,6,1; 1,69,41,8,1; 1,348,293,67,10,1; ... T(3,2)=4 because we have (13)2, 2(13), (23)1, 3(12), where the parentheses surround runs of length 2.
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CROSSREFS
| Row sums give A064314. Cf. A064315.
Column k=2 yields A000303, column k=3 yields A000402, column 4 yields A000434.
Sequence in context: A155826 A010320 A152571 * A203846 A118185 A176483
Adjacent sequences: A008301 A008302 A008303 * A008305 A008306 A008307
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KEYWORD
| tabl,nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from David W. Wilson (davidwwilson(AT)comcast.net), Sep 07 2001
Better description from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 08 2004
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