cp's OEIS Frontend

A316396 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value of nine.

%I A316396 #5 Jul 01 2018 18:05:51
%S A316396 1,9,2071,20845,1553153,17662969,908651571,11670560732,512693233164,
%T A316396 7392808621010,303061463720474,4869546964922509,194661534866479194,
%U A316396 3459210686800253224,138131753631241199208,2695708505172764233290,109038227244360661170616
%N A316396 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value of nine.
%H A316396 Alois P. Heinz, <a href="/A316396/b316396.txt">Table of n, a(n) for n = 9..451</a>
%F A316396 a(n) = A262171(n) - A262170(n).
%p A316396 b:= proc(u, o, c, k) option remember;
%p A316396       `if`(c<0 or c>k, 0, `if`(u+o=0, 1,
%p A316396        add(b(u-j, o-1+j, c+1, k), j=1..u)+
%p A316396        add(b(u+j-1, o-j, c-1, k), j=1..o)))
%p A316396     end:
%p A316396 a:= n-> b(n, 0$2, 9)-b(n, 0$2, 8):
%p A316396 seq(a(n), n=9..25);
%Y A316396 Column k=9 of A258829.
%Y A316396 Cf. A262170, A262171.
%K A316396 nonn
%O A316396 9,2
%A A316396 _Alois P. Heinz_, Jul 01 2018