A230055 Number of permutations of [n] in which the longest increasing run has length 7.

1, 14, 181, 2360, 32010, 456720, 6881160, 109546009, 1841298059, 32629877967, 608572228291, 11923667699474, 244964063143590, 5267496652725480, 118348438201424761, 2773714509551524351, 67705791536824698266, 1718769199589362743761, 45314525515737783596251

Offset: 7

Author

Alois P. Heinz, Oct 07 2013

Keywords

• nonn

Examples

			a(7) = 1: 1234567.
a(8) = 14: 12345687, 12345786, 12346785, 12356784, 12456783, 13456782, 21345678, 23456781, 31245678, 41235678, 51234678, 61234578, 71234568, 81234567.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..200

Crossrefs

Column k=7 of A008304.

Programs

Maple

b:= proc(u, o, t, k) option remember; `if`(u+o=0, 1,
      `if`(t b(n, 0, 0, 7)-b(n, 0, 0, 6):
seq(a(n), n=7..30);

Mathematica

b[u_, o_, t_, k_] := b[u, o, t, k] = If[u + o == 0, 1, If[t < k - 1, Sum[b[u + j - 1, o - j, t + 1, k], {j, 1, o}], 0] + Sum[b[u - j, o + j - 1, 0, k], {j, 1, u}]];
a[n_] := b[n, 0, 0, 7] - b[n, 0, 0, 6];
Table[a[n], {n, 7, 30}] (* Jean-François Alcover, Jul 19 2018, after Alois P. Heinz *)

Formula

a(n) = A230051(n) - A177553(n).

E.g.f.: 1/Sum_{n>=0} (8*n+1-x)*x^(8*n)/(8*n+1)! - 1/Sum_{n>=0} (7*n+1-x)*x^(7*n)/(7*n+1)!.