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A243875 Number of Dyck paths of semilength n having exactly 5 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).

%I A243875 #5 Jun 13 2014 16:43:21
%S A243875 1,7,40,219,1161,6035,30816,154815,766711,3749225,18128129,86772929,
%T A243875 411599785,1936434085,9042584447,41939926492,193310490160,
%U A243875 885917766448,4038628790596,18320941855600,82734637234636,372039593944604,1666387342165538,7436328773819975
%N A243875 Number of Dyck paths of semilength n having exactly 5 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).
%H A243875 Alois P. Heinz, <a href="/A243875/b243875.txt">Table of n, a(n) for n = 21..400</a>
%p A243875 b:= proc(x, y, t) option remember; `if`(y<0 or y>x, 0, `if`(x=0, 1,
%p A243875      series(b(x-1, y+1, [2, 2, 4, 5, 6, 2, 4, 2, 10, 2][t])+`if`(t=10,
%p A243875       z, 1)*b(x-1, y-1, [1, 3, 1, 3, 3, 7, 8, 9, 1, 3][t]), z, 6)))
%p A243875     end:
%p A243875 a:= n-> coeff(b(2*n, 0, 1), z, 5):
%p A243875 seq(a(n), n=21..50);
%Y A243875 Column k=5 of A243881.
%K A243875 nonn
%O A243875 21,2
%A A243875 _Alois P. Heinz_, Jun 13 2014