%I #6 Sep 09 2017 11:35:15
%S 1,10,109,857,5915,36063,202712,1066920,5342964,25702079,119712521,
%T 542946033,2408776681,10490222605,44973252446,190237502710,
%U 795469360671,3293109382032,13514583025521,55040336697141,222657353371499,895378574918015,3581602988204833
%N Number of symmetrically unique Dyck paths of semilength n and height ten.
%H Alois P. Heinz, <a href="/A291894/b291894.txt">Table of n, a(n) for n = 10..1000</a>
%H <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (20, -163, 650, -932, -2412, 12511, -16162, -16958, 75036, -66056, -52648, 146758, -84808, -40683, 74434, -29145, -4672, 7199, -2242, 286, -12).
%F 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)).
%Y Column k=10 of A291883.
%K nonn,easy
%O 10,2
%A _Alois P. Heinz_, Sep 05 2017