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Search: id:A006157
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| A006157 |
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a(n+1) = (n-1) a(n) +n.n!.
(Formerly M3950)
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+0
5
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| 1, 5, 28, 180, 1320, 10920, 100800, 1028160, 11491200, 139708800, 1836172800, 25945920000, 392302310400, 6320426112000, 108101081088000, 1956280854528000
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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Number of ascending runs of length at least two in all permutations of [n]. Example: a(3)=5 because we have (123), (13)2, 3(12), 2(13), (23)1, and 321, where the ascending runs of length at least 2 are shown between parentheses. - Emeric Deutsch and Ira Gessel (deutsch(AT)duke.poly.edu), Sep 07 2004
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REFERENCES
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J. Francon, Histoires de fichiers, RAIRO Informatique Th\'{e}orique et Applications, 12 (1978), 49-62.
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FORMULA
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(2n-1)/6 * n!.
E.g.f. = x^2*(3-x)/[6(1-x)^2]. - Emeric Deutsch and Ira Gessel (deutsch(AT)duke.poly.edu), Sep 07 2004
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CROSSREFS
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Cf. A014484.
Adjacent sequences: A006154 A006155 A006156 this_sequence A006158 A006159 A006160
Sequence in context: A082031 A020081 A095676 this_sequence A123776 A070779 A024065
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KEYWORD
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nonn,easy
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AUTHOR
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njas, Simon Plouffe (plouffe(AT)math.uqam.ca)
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