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)).

1, 11, 86, 611, 4106, 26508, 165608, 1005693, 5958138, 34538560, 196383607, 1097479232, 6038391492, 32757730552, 175436127352, 928559489820, 4861821384020, 25202877769350, 129444778524955, 659155791410730, 3329785315219783, 16695460286688023, 83126852562101708

Offset: 37

Author

Alois P. Heinz, Jun 13 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 37..400

Crossrefs

Column k=9 of A243881.

Programs

Maple

b:= proc(x, y, t) option remember; `if`(y<0 or y>x, 0, `if`(x=0, 1,
     series(b(x-1, y+1, [2, 2, 4, 5, 6, 2, 4, 2, 10, 2][t])+`if`(t=10,
      z, 1)*b(x-1, y-1, [1, 3, 1, 3, 3, 7, 8, 9, 1, 3][t]), z, 10)))
    end:
a:= n-> coeff(b(2*n, 0, 1), z, 9):
seq(a(n), n=37..65);