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A243876 Number of Dyck paths of semilength n having exactly 6 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).

%I A243876 #5 Jun 13 2014 16:40:36
%S A243876 1,8,50,295,1674,9255,50037,265190,1381151,7083239,35832547,179064335,
%T A243876 885033494,4330974280,21002926804,101014451257,482163988802,
%U A243876 2285470580378,10763603536650,50390267987583,234599001141494,1086577533281204,5008393400154248
%N A243876 Number of Dyck paths of semilength n having exactly 6 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).
%H A243876 Alois P. Heinz, <a href="/A243876/b243876.txt">Table of n, a(n) for n = 25..400</a>
%p A243876 b:= proc(x, y, t) option remember; `if`(y<0 or y>x, 0, `if`(x=0, 1,
%p A243876      series(b(x-1, y+1, [2, 2, 4, 5, 6, 2, 4, 2, 10, 2][t])+`if`(t=10,
%p A243876       z, 1)*b(x-1, y-1, [1, 3, 1, 3, 3, 7, 8, 9, 1, 3][t]), z, 7)))
%p A243876     end:
%p A243876 a:= n-> coeff(b(2*n, 0, 1), z, 6):
%p A243876 seq(a(n), n=25..55);
%Y A243876 Column k=6 of A243881.
%K A243876 nonn
%O A243876 25,2
%A A243876 _Alois P. Heinz_, Jun 13 2014