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%I #5 Jul 01 2018 18:47:38
%S 1,10,4127,45562,4719041,58003461,3795919780,52052335254,
%T 2772611610514,42268105493955,2037044419366071,34333238955892416,
%U 1578674337291922196,29239755067140936242,1321207703588407017510,26733500408009431631728,1208079945873987947779946
%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 ten.
%H Alois P. Heinz, <a href="/A316397/b316397.txt">Table of n, a(n) for n = 10..451</a>
%F a(n) = A262172(n) - A262171(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, 10)-b(n, 0$2, 9):
%p seq(a(n), n=10..26);
%Y Column k=10 of A258829.
%Y Cf. A262171, A262172.
%K nonn
%O 10,2
%A _Alois P. Heinz_, Jul 01 2018