A291893 Number of symmetrically unique Dyck paths of semilength n and height nine.

1, 9, 89, 639, 4082, 23191, 122381, 607944, 2887756, 13229876, 58898404, 256121253, 1092452270, 4585149401, 18985099139, 77707979700, 314944855135, 1265638606115, 5048705160315, 20010229736469, 78861912700117, 309252947330313, 1207359268831473

Offset: 9

Author

Alois P. Heinz, Sep 05 2017

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..1000
• Index entries for linear recurrences with constant coefficients, signature (18, -129, 428, -339, -2154, 7022, -5004, -13608, 31128, -13587, -27364, 38529, -11230, -11610, 11180, -3805, 550, -25).

Crossrefs

Column k=9 of A291883.

Formula

G.f.: -x^9*(-1+9*x-56*x^2+230*x^3-548*x^4+741*x^5-564*x^6+238*x^7-55*x^8+5*x^9) / ((x^2-3*x+1) *(5*x^2-5*x+1) *(5*x^4-5*x^2+1) *(x^5-3*x^4-3*x^3+4*x^2+x-1) *(x^5-15*x^4+35*x^3-28*x^2+9*x-1)).