%I #13 Oct 16 2017 11:45:35

%S 0,1,22,223,1344,5727,19193,54046,133476,297633,611644,1175845,

%T 2138500,3711279,6187767,9965276,15570232,23687409,35193282,51193771,

%U 73066648,102508879,141589173,192806010,259151420,344180785,452088936,587792817,757020988,966410239

%N Number of 8-leaf rooted trees with n levels.

%H Alois P. Heinz, <a href="/A290362/b290362.txt">Table of n, a(n) for n = 0..1000</a>

%H B. A. Huberman and T. Hogg, <a href="https://doi.org/10.1016/0167-2789(86)90308-1">Complexity and adaptation</a>, Evolution, games and learning (Los Alamos, N.M., 1985). Phys. D 22 (1986), no. 1-3, 376-384.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).

%F G.f.: (5*x^5+57*x^4+120*x^3+75*x^2+14*x+1)*x / (x-1)^8.

%F a(n) = (272*n^7+273*n^6+749*n^5+1365*n^4+1043*n^3+882*n^2+456*n)/7!.

%p a:= n-> ((((((272*n+273)*n+749)*n+1365)*n+1043)*n+882)*n+456)*n/7!:

%p seq(a(n), n=0..40);

%t LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{0,1,22,223,1344,5727,19193,54046},30] (* _Harvey P. Dale_, Oct 16 2017 *)

%Y Row n=8 of A290353.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, Jul 28 2017