A289418 Number of Dyck paths of semilength n and height exactly 5.

1, 9, 52, 247, 1053, 4199, 16017, 59224, 214058, 760487, 2665884, 9246276, 31793724, 108548332, 368400045, 1244027317, 4182854728, 14012220027, 46789129817, 155798575851, 517500496981, 1715190689420, 5673820630478, 18736674281091, 61779282616728

Offset: 5

Author

Alois P. Heinz, Jul 06 2017

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-29,40,-22,3).

Crossrefs

Column k=5 of A080936.

Programs

Mathematica

LinearRecurrence[{9,-29,40,-22,3},{1,9,52,247,1053},40] (* Harvey P. Dale, Dec 07 2018 *)

Formula

G.f.: -x^5/((x-1)*(3*x-1)*(x^3-6*x^2+5*x-1)).