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Number of Dyck paths of semilength n such that no level has more than ten peaks.
2

%I #6 Jun 03 2017 19:03:02

%S 1,1,2,5,14,42,132,429,1430,4862,16796,58785,208010,742873,2674282,

%T 9693840,35351966,129613793,477477188,1766446640,6560091544,

%U 24446776958,91389820234,342624437057,1287886748877,4852692487519,18325298874477,69344013520559

%N Number of Dyck paths of semilength n such that no level has more than ten peaks.

%H Alois P. Heinz, <a href="/A287974/b287974.txt">Table of n, a(n) for n = 0..1000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lattice_path#Counting_lattice_paths">Counting lattice paths</a>

%F a(n) = A287847(n,10).

%F a(n) = A000108(n) for n <= 10.

%Y Column k=10 of A287847.

%Y Cf. A000108.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Jun 03 2017