A230236 Number of permutations of [n] in which the longest increasing run has length 10.

1, 20, 349, 5954, 103194, 1845480, 34288800, 663848640, 13406178240, 282398538240, 6201593613645, 141859542537845, 3376683552323421, 83546513273754977, 2146303277645066980, 57187254952684274700, 1578640101972070456800, 45101111852055549981600

Offset

10,2

Links

Alois P. Heinz, Table of n, a(n) for n = 10..200

Formula

E.g.f.: 1/Sum_{n>=0} (11*n+1-x)*x^(11*n)/(11*n+1)! - 1/Sum_{n>=0} (10*n+1-x)*x^(10*n)/(10*n+1)!.

a(n) = A230233(n) - A230232(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, 10)-b(n, 0, 0, 9):
seq(a(n), n=10..30);

Crossrefs

Column k=10 of A008304.

Sequence in context: A268787 A272183 A005748 * A093144 A285393 A156455

Adjacent sequences: A230233 A230234 A230235 * A230237 A230238 A230239

Keyword

nonn

Author

Alois P. Heinz, Oct 12 2013

Status

approved