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A288542 Number of Dyck paths of semilength n such that the minimal number of peaks over all positive levels equals three.

%I A288542 #6 Jun 12 2017 08:59:36
%S A288542 1,0,0,0,4,29,90,188,345,825,3089,13450,54526,198846,668430,2155731,
%T A288542 6963768,23265733,81163559,292726843,1073684818,3953422052,
%U A288542 14517741411,53096290021,193719344526,706944953011,2586796240687,9505841335788,35102295346482
%N A288542 Number of Dyck paths of semilength n such that the minimal number of peaks over all positive levels equals three.
%H A288542 Alois P. Heinz, <a href="/A288542/b288542.txt">Table of n, a(n) for n = 3..300</a>
%H A288542 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lattice_path#Counting_lattice_paths">Counting lattice paths</a>
%e A288542 : a(7) = 4:
%e A288542 :
%e A288542 :        /\/\/\        /\/\/\        /\/\/\        /\/\/\
%e A288542 : /\/\/\/      \  /\/\/      \/\  /\/      \/\/\  /      \/\/\/\  .
%Y A288542 Column k=3 of A288387.
%Y A288542 Cf. A000108.
%K A288542 nonn
%O A288542 3,5
%A A288542 _Alois P. Heinz_, Jun 11 2017