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%I #5 Jul 01 2018 15:12:31
%S 1,6,261,1890,52022,455231,11174035,116105272,2810232512,34036483163,
%T 844691910962,11731978216291,303637667232802,4769379288424677,
%U 129700918311614279,2277005590881369266,65261900211279910831,1267764017301809851710,38324737795523150842616
%N Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value of six.
%H Alois P. Heinz, <a href="/A316393/b316393.txt">Table of n, a(n) for n = 6..452</a>
%F a(n) = A262168(n) - A262167(n).
%p b:= proc(u, o, c, k) option remember;
%p `if`(c<0 or c>k, 0, `if`(u+o=0, 1,
%p add(b(u-j, o-1+j, c+1, k), j=1..u)+
%p add(b(u+j-1, o-j, c-1, k), j=1..o)))
%p end:
%p a:= n-> b(n, 0$2, 6)-b(n, 0$2, 5):
%p seq(a(n), n=6..24);
%Y Column k=6 of A258829.
%Y Cf. A262167, A262168.
%K nonn
%O 6,2
%A _Alois P. Heinz_, Jul 01 2018
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