cp's OEIS Frontend

A243877 Number of Dyck paths of semilength n having exactly 7 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).

%I A243877 #5 Jun 13 2014 16:38:11
%S A243877 1,9,61,385,2323,13583,77363,430573,2348528,12584052,66372328,
%T A243877 345160962,1772302098,8996192858,45189272314,224832198163,
%U A243877 1108842335240,5424622033040,26340438937256,127018289627132,608569050945950,2898295732654434,13725710735084610
%N A243877 Number of Dyck paths of semilength n having exactly 7 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).
%H A243877 Alois P. Heinz, <a href="/A243877/b243877.txt">Table of n, a(n) for n = 29..400</a>
%p A243877 b:= proc(x, y, t) option remember; `if`(y<0 or y>x, 0, `if`(x=0, 1,
%p A243877      series(b(x-1, y+1, [2, 2, 4, 5, 6, 2, 4, 2, 10, 2][t])+`if`(t=10,
%p A243877       z, 1)*b(x-1, y-1, [1, 3, 1, 3, 3, 7, 8, 9, 1, 3][t]), z, 8)))
%p A243877     end:
%p A243877 a:= n-> coeff(b(2*n, 0, 1), z, 7):
%p A243877 seq(a(n), n=29..60);
%Y A243877 Column k=7 of A243881.
%K A243877 nonn
%O A243877 29,2
%A A243877 _Alois P. Heinz_, Jun 13 2014