A230234 Number of permutations of [n] in which the longest increasing run has length 8.

1, 16, 231, 3322, 49236, 761904, 12372360, 211170960, 3788091451, 71356438043, 1409672722481, 29163603260677, 630867328411136, 14247689906846928, 335437110802718232, 8220763598490652440, 209435069840238717949, 5539287889970005834349, 151909981369978722092098

Offset

8,2

Links

Alois P. Heinz, Table of n, a(n) for n = 8..170

Formula

E.g.f.: 1/Sum_{n>=0} (9*n+1-x)*x^(9*n)/(9*n+1)! - 1/Sum_{n>=0} (8*n+1-x)*x^(8*n)/(8*n+1)!.

a(n) = A230231(n) - A230051(n).

Maple

b:= proc(u, o, t, k) option remember; `if`(u+o=0, 1,
      `if`(t<k-1, add(b(u+j-1, o-j, t+1, k), j=1..o), 0)+
      add(b(u-j, o+j-1, 0, k), j=1..u))
    end:
a:= n-> b(n, 0, 0, 8)-b(n, 0, 0, 7):
seq(a(n), n=8..30);

Crossrefs

Column k=8 of A008304.

Sequence in context: A048445 A028340 A166903 * A274467 A119463 A292341

Adjacent sequences: A230231 A230232 A230233 * A230235 A230236 A230237

Keyword

nonn

Author

Alois P. Heinz, Oct 12 2013

Status

approved