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A243878 Number of Dyck paths of semilength n having exactly 8 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).

%I A243878 #5 Jun 13 2014 16:36:48
%S A243878 1,10,73,490,3127,19249,115021,669745,3812716,21277658,116666435,
%T A243878 629665898,3350420024,17599292330,91368992279,469293511892,
%U A243878 2386777084592,12029136326922,60118399193577,298121360285805,1467661404628893,7176555449003580,34870090954789419
%N A243878 Number of Dyck paths of semilength n having exactly 8 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).
%H A243878 Alois P. Heinz, <a href="/A243878/b243878.txt">Table of n, a(n) for n = 33..400</a>
%p A243878 b:= proc(x, y, t) option remember; `if`(y<0 or y>x, 0, `if`(x=0, 1,
%p A243878      series(b(x-1, y+1, [2, 2, 4, 5, 6, 2, 4, 2, 10, 2][t])+`if`(t=10,
%p A243878       z, 1)*b(x-1, y-1, [1, 3, 1, 3, 3, 7, 8, 9, 1, 3][t]), z, 9)))
%p A243878     end:
%p A243878 a:= n-> coeff(b(2*n, 0, 1), z, 8):
%p A243878 seq(a(n), n=33..60);
%Y A243878 Column k=8 of A243881.
%K A243878 nonn
%O A243878 33,2
%A A243878 _Alois P. Heinz_, Jun 13 2014