A288390 - OEIS

%I #10 May 09 2021 02:16:44

%S 1,1,1,2,5,11,28,79,215,629,1809,5426,16470,50317,155322,483924,

%T 1521732,4822068,15360504,49144119,158049374,510824766,1657541406,

%U 5396486955,17626155846,57754129486,189807753894,625506513608,2066420369017,6842171033524

%N Number of Dyck paths of semilength n such that the number of peaks in each positive level is a term of this sequence.

%H Alois P. Heinz, <a href="/A288390/b288390.txt">Table of n, a(n) for n = 0..600</a>

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

%e a(4) = 5:

%e .

%e .           /\      /\      /\          /\/\    /\/\

%e .      /\/\/  \  /\/  \/\  /  \/\/\  /\/    \  /    \/\  .

%Y Cf. A000108, A288388.

%K nonn

%O 0,4

%A _Alois P. Heinz_, Jun 08 2017