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Number of ascent sequences of length n with exactly four flat steps.
3

%I #9 Feb 10 2015 06:54:56

%S 1,5,30,175,1120,7686,56910,452760,3858525,35101495,339725386,

%T 3487023540,37846867240,433186049100,5215583431800,65904645333720,

%U 872154648378075,12063864339947700,174104719888432025,2617216790440934220,40916672402313971340

%N Number of ascent sequences of length n with exactly four flat steps.

%H Joerg Arndt and Alois P. Heinz, <a href="/A242157/b242157.txt">Table of n, a(n) for n = 5..140</a>

%F a(n) ~ Pi^(11/2)/(864*sqrt(3)*exp(Pi^2/12)) * (6/Pi^2)^n * n! * sqrt(n). - _Vaclav Kotesovec_, Aug 27 2014

%t b[n_, i_, t_] := b[n, i, t] = If[n == 0, 1, Expand[Sum[ If[j == i, x, 1]*b[n - 1, j, t + If[j > i, 1, 0]], {j, 0, t + 1}]]]; a[n_] := Coefficient[b[n, -1, -1], x, 4]; Table[a[n], {n, 5, 30}] (* _Jean-François Alcover_, Feb 10 2015, after A242153 *)

%Y Column k=4 of A242153.

%K nonn

%O 5,2

%A _Joerg Arndt_ and _Alois P. Heinz_, May 05 2014