A000467 Number of permutations of [n] in which the longest increasing run has length 6.

0, 0, 0, 0, 0, 1, 12, 137, 1602, 19710, 257400, 3574957, 52785901, 827242933, 13730434111, 240806565782, 4452251786946, 86585391630673, 1767406549387381, 37790452850585180, 844817788372455779, 19711244788916894489, 479203883157602851294

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

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

• 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.

Crossrefs

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

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

Programs

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-François Alcover, Feb 08 2016, after Alois P. Heinz in A008304 *)

Extensions

Edited and extended by Max Alekseyev, May 20 2012