cp's OEIS Frontend

A262172 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= 10.

%I A262172 #4 Sep 14 2015 18:01:59
%S A262172 1,1,2,5,20,87,522,3271,26168,214955,2149550,21881102,262573224,
%T A262172 3191352956,44678941384,631531613445,10104505815120,162875348137045,
%U A262172 2931756266466810,53078841003479472,1061576820069589440,21327553502651079406,469206177058323746932
%N A262172 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= 10.
%H A262172 Alois P. Heinz, <a href="/A262172/b262172.txt">Table of n, a(n) for n = 0..200</a>
%F A262172 a(n) = A262163(n,10).
%p A262172 b:= proc(u, o, c) option remember; `if`(c<0 or c>10, 0, `if`(u+o=0,
%p A262172        x^c, (p-> add(coeff(p, x, i)*x^max(i, c), i=0..10))(add(
%p A262172        b(u-j, o-1+j, c-1), j=1..u)+add(b(u+j-1, o-j, c+1), j=1..o))))
%p A262172     end:
%p A262172 a:= n-> (p-> add(coeff(p, x, i), i=0..min(n, 10)))(b(0, n, 0)):
%p A262172 seq(a(n), n=0..25);
%Y A262172 Column k=10 of A262163.
%K A262172 nonn
%O A262172 0,3
%A A262172 _Alois P. Heinz_, Sep 13 2015