A291894 Number of symmetrically unique Dyck paths of semilength n and height ten.

1, 10, 109, 857, 5915, 36063, 202712, 1066920, 5342964, 25702079, 119712521, 542946033, 2408776681, 10490222605, 44973252446, 190237502710, 795469360671, 3293109382032, 13514583025521, 55040336697141, 222657353371499, 895378574918015, 3581602988204833

Offset

10,2

Links

Alois P. Heinz, Table of n, a(n) for n = 10..1000

Index entries for linear recurrences with constant coefficients, signature (20, -163, 650, -932, -2412, 12511, -16162, -16958, 75036, -66056, -52648, 146758, -84808, -40683, 74434, -29145, -4672, 7199, -2242, 286, -12).

Formula

G.f.: x^10*(1-10*x +72*x^2 -343*x^3 +974*x^4 -1664*x^5 +1744*x^6 -1117*x^7 +413*x^8 -70*x^9 +x^11) / ((x-1) *(3*x-1) *(2*x-1) *(x^2-4*x+1) *(2*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) *(x^4-4*x^2+1)).

Crossrefs

Column k=10 of A291883.

Sequence in context: A246073 A261920 A024527 * A217322 A198700 A320094

Adjacent sequences: A291891 A291892 A291893 * A291895 A291896 A291897

Keyword

nonn,easy

Author

Alois P. Heinz, Sep 05 2017

Status

approved