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%I #11 Jan 09 2019 15:48:31
%S 0,1,42,817,8429,55627,268272,1030101,3331117,9425128,23970089,
%T 55880968,121188860,247272012,478904297,886654486,1578265414,
%U 2713745819,4525019252,7341094011,11619845543,17987638185,27288156478,40641967587,59518495595,85822255610
%N Number of 10-leaf rooted trees with n levels.
%H Alois P. Heinz, <a href="/A290364/b290364.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_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F G.f.: (13*x^7+312*x^6+1835*x^5+3272*x^4+2029*x^3+442*x^2+32*x+1)*x / (x-1)^10.
%F a(n) = (7936*n^9 +4635*n^8 +24756*n^7 +43974*n^6 +65352*n^5 +60795*n^4 +81524*n^3 +72036*n^2 +1872*n)/9!.
%p a:= n-> ((((((((7936*n+4635)*n+24756)*n+43974)*n+65352)*n
%p +60795)*n+81524)*n+72036)*n+1872)*n/9!:
%p seq(a(n), n=0..40);
%t LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{0,1,42,817,8429,55627,268272,1030101,3331117,9425128},30] (* _Harvey P. Dale_, Jan 09 2019 *)
%Y Row n=10 of A290353.
%K nonn,easy
%O 0,3
%A _Alois P. Heinz_, Jul 28 2017
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