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A243879 Number of Dyck paths of semilength n having exactly 9 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).

%I A243879 #5 Jun 13 2014 16:33:58
%S A243879 1,11,86,611,4106,26508,165608,1005693,5958138,34538560,196383607,
%T A243879 1097479232,6038391492,32757730552,175436127352,928559489820,
%U A243879 4861821384020,25202877769350,129444778524955,659155791410730,3329785315219783,16695460286688023,83126852562101708
%N A243879 Number of Dyck paths of semilength n having exactly 9 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).
%H A243879 Alois P. Heinz, <a href="/A243879/b243879.txt">Table of n, a(n) for n = 37..400</a>
%p A243879 b:= proc(x, y, t) option remember; `if`(y<0 or y>x, 0, `if`(x=0, 1,
%p A243879      series(b(x-1, y+1, [2, 2, 4, 5, 6, 2, 4, 2, 10, 2][t])+`if`(t=10,
%p A243879       z, 1)*b(x-1, y-1, [1, 3, 1, 3, 3, 7, 8, 9, 1, 3][t]), z, 10)))
%p A243879     end:
%p A243879 a:= n-> coeff(b(2*n, 0, 1), z, 9):
%p A243879 seq(a(n), n=37..65);
%Y A243879 Column k=9 of A243881.
%K A243879 nonn
%O A243879 37,2
%A A243879 _Alois P. Heinz_, Jun 13 2014