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

Author

Alois P. Heinz, Jul 06 2017

Keywords

• nonn
• easy

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).

Crossrefs

Column k=7 of A080936.

Programs

Mathematica

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

Formula

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