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

%I #6 Jun 03 2017 19:03:38

%S 1,1,2,5,14,42,132,429,1430,4862,16795,58784,207987,742760,2673592,

%T 9690220,35333404,129522165,477035494,1764359882,6550391672,

%U 24402303601,91188289504,341720434791,1283867554724,4834962472637,18247627360326,69005857450243

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

%H Alois P. Heinz, <a href="/A287973/b287973.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,9).

%F a(n) = A000108(n) for n <= 9.

%Y Column k=9 of A287847.

%Y Cf. A000108.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Jun 03 2017