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A243874 Number of Dyck paths of semilength n having exactly 4 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).

%I A243874 #5 Jun 13 2014 16:45:27
%S A243874 1,6,31,156,766,3717,17812,84342,395152,1833853,8438976,38540936,
%T A243874 174819086,788082431,3532770025,15755543925,69937932805,309113716505,
%U A243874 1360804143915,5968626187120,26089764842864,113680654898844,493874661384094,2139660006480909
%N A243874 Number of Dyck paths of semilength n having exactly 4 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).
%H A243874 Alois P. Heinz, <a href="/A243874/b243874.txt">Table of n, a(n) for n = 17..400</a>
%p A243874 b:= proc(x, y, t) option remember; `if`(y<0 or y>x, 0, `if`(x=0, 1,
%p A243874      series(b(x-1, y+1, [2, 2, 4, 5, 6, 2, 4, 2, 10, 2][t])+`if`(t=10,
%p A243874       z, 1)*b(x-1, y-1, [1, 3, 1, 3, 3, 7, 8, 9, 1, 3][t]), z, 5)))
%p A243874     end:
%p A243874 a:= n-> coeff(b(2*n, 0, 1), z, 4):
%p A243874 seq(a(n), n=17..45);
%Y A243874 Column k=4 of A243881.
%K A243874 nonn
%O A243874 17,2
%A A243874 _Alois P. Heinz_, Jun 13 2014