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

Author

Alois P. Heinz, Oct 12 2013

Keywords

• nonn

Links

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

Crossrefs

Column k=9 of A008304.

Programs

Maple

b:= proc(u, o, t, k) option remember; `if`(u+o=0, 1,
      `if`(t b(n, 0, 0, 9)-b(n, 0, 0, 8):
seq(a(n), n=9..30);

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).