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

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