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A000467 Number of permutations of [n] in which the longest increasing run has length 6.
(Formerly M4868 N2083)
6
0, 0, 0, 0, 0, 1, 12, 137, 1602, 19710, 257400, 3574957, 52785901, 827242933, 13730434111, 240806565782, 4452251786946, 86585391630673, 1767406549387381, 37790452850585180, 844817788372455779, 19711244788916894489, 479203883157602851294 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

REFERENCES

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).

LINKS

Max Alekseyev, Table of n, a(n) for n = 1..100

Max A. Alekseyev, On the number of permutations with bounded run lengths, arXiv preprint arXiv:1205.4581 [math.CO], 2012.

MATHEMATICA

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-Fran├žois Alcover, Feb 08 2016, after Alois P. Heinz in A008304 *)

CROSSREFS

Column 6 of A008304. Other columns: A000303, A000402, A000434, A000456.

Cf. A001250, A001251, A001252, A001253, A010026, A211318.

Sequence in context: A189501 A216081 A264503 * A059517 A243966 A097167

Adjacent sequences:  A000464 A000465 A000466 * A000468 A000469 A000470

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Edited and extended by Max Alekseyev, May 20 2012

STATUS

approved

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Last modified June 29 06:43 EDT 2016. Contains 274294 sequences.