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%I #4 Sep 14 2015 17:21:53
%S 1,1,2,5,20,87,522,3271,26168,214955,2149549,21881092,262569097,
%T 3191307394,44674222343,631473609984,10100709895340,162823295801791,
%U 2928983654856296,53036572897985517,1059539775650223369,21293220263695186990,467627502721031824736
%N Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= 9.
%H Alois P. Heinz, <a href="/A262171/b262171.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = A262163(n,9).
%p b:= proc(u, o, c) option remember; `if`(c<0 or c>9, 0, `if`(u+o=0,
%p x^c, (p-> add(coeff(p, x, i)*x^max(i, c), i=0..9))(add(
%p b(u-j, o-1+j, c-1), j=1..u)+add(b(u+j-1, o-j, c+1), j=1..o))))
%p end:
%p a:= n-> (p-> add(coeff(p, x, i), i=0..min(n, 9)))(b(0, n, 0)):
%p seq(a(n), n=0..25);
%Y Column k=9 of A262163.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Sep 13 2015