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A262164 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= 2.

%I A262164 #5 Sep 13 2015 19:28:29
%S A262164 1,1,2,4,16,54,324,1532,12256,74512,745120,5536752,66441024,583466480,
%T A262164 8168530720,82769713504,1324315416064,15208157533440,273746835601920,
%U A262164 3513491887566848,70269837751336960,996837786288583168,21930431298348829696,340730692136161864704
%N A262164 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= 2.
%H A262164 Alois P. Heinz, <a href="/A262164/b262164.txt">Table of n, a(n) for n = 0..464</a>
%F A262164 a(n) = A262163(n,2).
%p A262164 b:= proc(u, o, c) option remember; `if`(c<0 or c>2, 0, `if`(u+o=0,
%p A262164        x^c, (p-> add(coeff(p, x, i)*x^max(i, c), i=0..2))(add(
%p A262164        b(u-j, o-1+j, c-1), j=1..u)+add(b(u+j-1, o-j, c+1), j=1..o))))
%p A262164     end:
%p A262164 a:= n-> (p-> add(coeff(p, x, i), i=0..min(n, 2)))(b(0, n, 0)):
%p A262164 seq(a(n), n=0..25);
%Y A262164 Column k=2 of A262163.
%K A262164 nonn
%O A262164 0,3
%A A262164 _Alois P. Heinz_, Sep 13 2015