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A243880 Number of Dyck paths of semilength n having exactly 10 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).

%I A243880 #5 Jun 13 2014 16:32:26
%S A243880 1,12,100,749,5281,35641,232123,1466180,9017295,54172152,318732558,
%T A243880 1840668348,10452539055,58458147585,322425939233,1755834940554,
%U A243880 9450381436619,50317234401194,265235076809408,1385156654929038,7171253075566076,36826968212298201
%N A243880 Number of Dyck paths of semilength n having exactly 10 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).
%H A243880 Alois P. Heinz, <a href="/A243880/b243880.txt">Table of n, a(n) for n = 41..400</a>
%p A243880 b:= proc(x, y, t) option remember; `if`(y<0 or y>x, 0, `if`(x=0, 1,
%p A243880      series(b(x-1, y+1, [2, 2, 4, 5, 6, 2, 4, 2, 10, 2][t])+`if`(t=10,
%p A243880       z, 1)*b(x-1, y-1, [1, 3, 1, 3, 3, 7, 8, 9, 1, 3][t]), z, 11)))
%p A243880     end:
%p A243880 a:= n-> coeff(b(2*n, 0, 1), z, 10):
%p A243880 seq(a(n), n=41..70);
%Y A243880 Column k=10 of A243881.
%K A243880 nonn
%O A243880 41,2
%A A243880 _Alois P. Heinz_, Jun 13 2014