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A000456
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Number of permutations of [n] in which the longest increasing run has length 5.
(Formerly M4735 N2027)
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6
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0, 0, 0, 0, 1, 10, 99, 1024, 11304, 133669, 1695429, 23023811, 333840443, 5153118154, 84426592621, 1463941342191, 26793750988542, 516319125748337, 10451197169218523, 221738082618710329, 4921234092461339819, 114041894068935641488
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OFFSET
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1,6
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REFERENCES
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F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 261.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..450 (first 100 terms from Max Alekseyev)
Max A. Alekseyev, On the number of permutations with bounded run lengths, arXiv preprint arXiv:1205.4581, 2012.
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EXAMPLE
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a(6)=10 because we have (12346)5, (12356)4, (12456)3, (13456)2, (23456)1, 6(12345), 5(12346), 4(12356), 3(12456) and 2(13456), where the parentheses surround increasing runs of length 5.
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MATHEMATICA
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b[u_, o_, t_, k_] := b[u, o, t, k] = If[t == k, (u + o)!, If[Max[t, u] + o < k, 0, Sum[b[u + j - 1, o - j, t + 1, k], {j, 1, o}] + Sum[b[u - j, o + j - 1, 1, k], {j, 1, u}]]]; T[n_, k_] := b[0, n, 0, k] - b[0, n, 0, k + 1]; a[n_] := T[n, 5]; Array[a, 25] (* Jean-François Alcover, Feb 08 2016, after Alois P. Heinz in A008304 *)
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CROSSREFS
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Column 5 of A008304. Other columns: A000303, A000402, A000434, A000467.
Cf. A001250, A001251, A001252, A001253, A010026, A211318.
Sequence in context: A179557 A300000 A213454 * A138365 A190823 A187019
Adjacent sequences: A000453 A000454 A000455 * A000457 A000458 A000459
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Better description from Emeric Deutsch, May 08 2004
Edited and extended by Max Alekseyev, May 20 2012
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STATUS
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approved
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