%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