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%I #15 Aug 22 2019 17:40:38
%S 0,1,11,58,206,571,1337,2772,5244,9237,15367,24398,37258,55055,79093,
%T 110888,152184,204969,271491,354274,456134,580195,729905,909052,
%U 1121780,1372605,1666431,2008566,2404738,2861111,3384301,3981392,4659952,5428049,6294267
%N Number of 6-leaf rooted trees with n levels.
%H Alois P. Heinz, <a href="/A290360/b290360.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/Ro#rooted">Index entries for sequences related to rooted trees</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F G.f.: (3*x+1)*(x+1)^2*x / (x-1)^6.
%F a(n) = (4*n^5+5*n^4+10*n^3+10*n^2+n)/30.
%p a:= n-> ((((4*n+5)*n+10)*n+10)*n+1)*n/30:
%p seq(a(n), n=0..40);
%t LinearRecurrence[{6,-15,20,-15,6,-1},{0,1,11,58,206,571},40] (* _Harvey P. Dale_, Aug 22 2019 *)
%Y Row n=6 of A290353.
%K nonn,easy
%O 0,3
%A _Alois P. Heinz_, Jul 28 2017
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