cp's OEIS Frontend

A262169 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= 7.

%I A262169 #4 Sep 14 2015 15:48:55
%S A262169 1,1,2,5,20,87,522,3271,26167,214946,2148500,21869553,262040897,
%T A262169 3184440794,44442180413,627992981034,9996086297542,161044694650665,
%U A262169 2877551846402242,52059368659632095,1031291013069584902,20699996793232418643,450130761784158558067
%N A262169 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= 7.
%H A262169 Alois P. Heinz, <a href="/A262169/b262169.txt">Table of n, a(n) for n = 0..451</a>
%F A262169 a(n) = A262163(n,7).
%p A262169 b:= proc(u, o, c) option remember; `if`(c<0 or c>7, 0, `if`(u+o=0,
%p A262169        x^c, (p-> add(coeff(p, x, i)*x^max(i, c), i=0..7))(add(
%p A262169        b(u-j, o-1+j, c-1), j=1..u)+add(b(u+j-1, o-j, c+1), j=1..o))))
%p A262169     end:
%p A262169 a:= n-> (p-> add(coeff(p, x, i), i=0..min(n, 7)))(b(0, n, 0)):
%p A262169 seq(a(n), n=0..25);
%Y A262169 Column k=7 of A262163.
%K A262169 nonn
%O A262169 0,3
%A A262169 _Alois P. Heinz_, Sep 13 2015