A230235 Number of permutations of [n] in which the longest increasing run has length 9.

1, 18, 287, 4512, 72540, 1209936, 21064680, 383685120, 7315701120, 145957544981, 3044416187213, 66312765615259, 1506481046115907, 35648661471454418, 877558860954150150, 22444760416001869200, 595702609788740888400, 16387438983202886695200

Offset

9,2

Links

Alois P. Heinz, Table of n, a(n) for n = 9..200

Formula

E.g.f.: 1/Sum_{n>=0} (10*n+1-x)*x^(10*n)/(10*n+1)! - 1/Sum_{n>=0} (9*n+1-x)*x^(9*n)/(9*n+1)!.

a(n) = A230232(n) - A230231(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, 9)-b(n, 0, 0, 8):
seq(a(n), n=9..30);

Crossrefs

Column k=9 of A008304.

Sequence in context: A245924 A368526 A035119 * A288959 A294327 A286725

Adjacent sequences: A230232 A230233 A230234 * A230236 A230237 A230238

Keyword

nonn

Author

Alois P. Heinz, Oct 12 2013

Status

approved