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

9,2

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).

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)).

Crossrefs

Column k=9 of A291883.

Sequence in context: A055410 A214616 A175371 * A217321 A111918 A064616

Adjacent sequences: A291890 A291891 A291892 * A291894 A291895 A291896

Keyword

nonn,easy

Author

Alois P. Heinz, Sep 05 2017

Status

approved