|
%I #5 Oct 13 2013 16:52:44
%S 1,20,349,5954,103194,1845480,34288800,663848640,13406178240,
%T 282398538240,6201593613645,141859542537845,3376683552323421,
%U 83546513273754977,2146303277645066980,57187254952684274700,1578640101972070456800,45101111852055549981600
%N Number of permutations of [n] in which the longest increasing run has length 10.
%H Alois P. Heinz, <a href="/A230236/b230236.txt">Table of n, a(n) for n = 10..200</a>
%F 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)!.
%F a(n) = A230233(n) - A230232(n).
%p b:= proc(u, o, t, k) option remember; `if`(u+o=0, 1,
%p `if`(t<k-1, add(b(u+j-1, o-j, t+1, k), j=1..o), 0)+
%p add(b(u-j, o+j-1, 0, k), j=1..u))
%p end:
%p a:= n-> b(n, 0, 0, 10)-b(n, 0, 0, 9):
%p seq(a(n), n=10..30);
%Y Column k=10 of A008304.
%K nonn
%O 10,2
%A _Alois P. Heinz_, Oct 12 2013
|
