A291891 Number of symmetrically unique Dyck paths of semilength n and height seven.

1, 7, 55, 319, 1705, 8238, 37674, 164229, 692627, 2843282, 11433826, 45212792, 176385132, 680452948, 2600725892, 9862321095, 37150333241, 139139984973, 518538211261, 1924077739700, 7112221384554, 26201080984497, 96233327019085, 352501632479306

Offset: 7

Author

Alois P. Heinz, Sep 05 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, -60, 84, 203, -807, 569, 1173, -2090, 480, 1046, -662, -16, 76, -8).

Crossrefs

Column k=7 of A291883.

Programs

Mathematica

CoefficientList[Series[-(6*x - 24*x^2 + 60*x^3 - 67*x^4 + 21*x^5 + x^6 + x^7 - 1)/((x - 1)*(2*x - 1)*(2*x^2 - 4*x + 1)*(x^3 + 3*x^2 - 1)*(x^3 - 9*x^2 + 6*x - 1)*(2*x^4 - 4*x^2 + 1)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Oct 14 2023 *)

Formula

G.f.: -x^7*(6*x-24*x^2+60*x^3-67*x^4+21*x^5+x^6+x^7-1) / ((x-1) *(2*x-1) *(2*x^2-4*x+1) *(x^3+3*x^2-1) *(x^3-9*x^2+6*x-1) *(2*x^4-4*x^2+1)).