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Number of Dyck paths of semilength n such that at least one positive level has no peaks.
2

%I #12 Jun 11 2017 15:57:29

%S 1,0,1,2,8,25,83,282,971,3386,11940,42504,152546,551426,2005930,

%T 7337901,26976726,99618976,369349607,1374391706,5131186060,

%U 19214759396,72152791729,271629133830,1024989876797,3876208984221,14688301498888,55763768987236,212077310097784

%N Number of Dyck paths of semilength n such that at least one positive level has no peaks.

%C a(0) = 1 by convention.

%H Alois P. Heinz, <a href="/A288539/b288539.txt">Table of n, a(n) for n = 0..300</a>

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

%e : a(3) = 2:

%e : /\

%e : /\/\ / \

%e : / \ / \ .

%Y Column k=0 of A288387.

%Y Cf. A000108.

%K nonn

%O 0,4

%A _Alois P. Heinz_, Jun 11 2017