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A000467
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Number of permutations of [n] in which the longest increasing run has length 6.
(Formerly M4868 N2083)
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6
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0, 0, 0, 0, 0, 1, 12, 137, 1602, 19710, 257400, 3574957, 52785901, 827242933, 13730434111, 240806565782, 4452251786946, 86585391630673, 1767406549387381, 37790452850585180, 844817788372455779, 19711244788916894489, 479203883157602851294
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OFFSET
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1,7
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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 [math.CO], 2012.
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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, 6]; Array[a, 23] (* Jean-François Alcover, Feb 08 2016, after Alois P. Heinz in A008304 *)
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CROSSREFS
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Column 6 of A008304. Other columns: A000303, A000402, A000434, A000456.
Cf. A001250, A001251, A001252, A001253, A010026, A211318.
Sequence in context: A351514 A216081 A264503 * A059517 A243966 A097167
Adjacent sequences: A000464 A000465 A000466 * A000468 A000469 A000470
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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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Edited and extended by Max Alekseyev, May 20 2012
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STATUS
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approved
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