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A230235 Number of permutations of [n] in which the longest increasing run has length 9.

%I A230235 #6 Oct 13 2013 12:00:06
%S A230235 1,18,287,4512,72540,1209936,21064680,383685120,7315701120,
%T A230235 145957544981,3044416187213,66312765615259,1506481046115907,
%U A230235 35648661471454418,877558860954150150,22444760416001869200,595702609788740888400,16387438983202886695200
%N A230235 Number of permutations of [n] in which the longest increasing run has length 9.
%H A230235 Alois P. Heinz, <a href="/A230235/b230235.txt">Table of n, a(n) for n = 9..200</a>
%F A230235 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)!.
%F A230235 a(n) = A230232(n) - A230231(n).
%p A230235 b:= proc(u, o, t, k) option remember; `if`(u+o=0, 1,
%p A230235       `if`(t<k-1, add(b(u+j-1, o-j, t+1, k), j=1..o), 0)+
%p A230235       add(b(u-j, o+j-1, 0, k), j=1..u))
%p A230235     end:
%p A230235 a:= n-> b(n, 0, 0, 9)-b(n, 0, 0, 8):
%p A230235 seq(a(n), n=9..30);
%Y A230235 Column k=9 of A008304.
%K A230235 nonn
%O A230235 9,2
%A A230235 _Alois P. Heinz_, Oct 12 2013