A289422 Number of Dyck paths of semilength n and height exactly 9.

1, 17, 168, 1267, 8099, 46305, 244412, 1215448, 5773812, 26457508, 117789057, 512231849, 2184870646, 9170250565, 37970054320, 155415748396, 629889111670, 2531276312305, 10097407871079, 40020455708541, 157723815500329, 618505879152961, 2414718498047580

Offset

9,2

Links

Alois P. Heinz, Table of n, a(n) for n = 9..1000

Index entries for linear recurrences with constant coefficients, signature (17,-121,468,-1068,1461,-1163,496,-95,5).

Formula

G.f.: -x^9/((x^2-3*x+1)*(5*x^2-5*x+1)*(x^5-15*x^4+35*x^3-28*x^2+9*x-1)).

Mathematica

LinearRecurrence[{17, -121, 468, -1068, 1461, -1163, 496, -95, 5}, {1, 17, 168, 1267, 8099, 46305, 244412, 1215448, 5773812}, 30] (* Harvey P. Dale, Sep 28 2018 *)

Crossrefs

Column k=9 of A080936.

Sequence in context: A299551 A362537 A124299 * A157688 A155658 A121037

Adjacent sequences: A289419 A289420 A289421 * A289423 A289424 A289425

Keyword

nonn,easy

Author

Alois P. Heinz, Jul 06 2017

Status

approved