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%I #8 Oct 13 2013 09:08:09
%S 1,16,231,3322,49236,761904,12372360,211170960,3788091451,71356438043,
%T 1409672722481,29163603260677,630867328411136,14247689906846928,
%U 335437110802718232,8220763598490652440,209435069840238717949,5539287889970005834349,151909981369978722092098
%N Number of permutations of [n] in which the longest increasing run has length 8.
%H Alois P. Heinz, <a href="/A230234/b230234.txt">Table of n, a(n) for n = 8..170</a>
%F E.g.f.: 1/Sum_{n>=0} (9*n+1-x)*x^(9*n)/(9*n+1)! - 1/Sum_{n>=0} (8*n+1-x)*x^(8*n)/(8*n+1)!.
%F a(n) = A230231(n) - A230051(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, 8)-b(n, 0, 0, 7):
%p seq(a(n), n=8..30);
%Y Column k=8 of A008304.
%K nonn
%O 8,2
%A _Alois P. Heinz_, Oct 12 2013