A289420 Number of Dyck paths of semilength n and height exactly 7.

1, 13, 102, 629, 3366, 16422, 75140, 328185, 1384345, 5685306, 22863861, 90420110, 352754930, 1360882980, 5201391077, 19724548877, 74300429926, 278279597781, 1037075511926, 3848154018734, 14224439297732, 52402156308977, 192466640908913, 705003243252722

Offset

7,2

Links

Alois P. Heinz, Table of n, a(n) for n = 7..1000

Index entries for linear recurrences with constant coefficients, signature (13,-67,174,-239,166,-50,4).

Formula

G.f.: -x^7/((x-1)*(2*x-1)*(2*x^2-4*x+1)*(x^3-9*x^2+6*x-1)).

Mathematica

LinearRecurrence[{13, -67, 174, -239, 166, -50, 4}, {1, 13, 102, 629, 3366, 16422, 75140}, 30] (* Harvey P. Dale, Jul 21 2019 *)

Crossrefs

Column k=7 of A080936.

Sequence in context: A117653 A004635 A369418 * A050670 A142318 A246511

Adjacent sequences: A289417 A289418 A289419 * A289421 A289422 A289423

Keyword

nonn,easy

Author

Alois P. Heinz, Jul 06 2017

Status

approved