%I #14 Sep 08 2022 08:45:01

%S 9,22950,9236700,1731510000,213034536000,20154167953920,

%T 1599866940672000,112412172128256000,7240640845838400000,

%U 437993205197708160000,25315591135036262860800

%N Number of labeled rooted trees with n nodes and 8 leaves.

%H Vincenzo Librandi, <a href="/A055309/b055309.txt">Table of n, a(n) for n = 9..200</a>

%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>

%F a(n) = n! * (n-8)^2*(n-7)^2*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(9*n^4 - 234*n^3 + 2211*n^2 - 8938*n + 12960)/234101145600. - _Vaclav Kotesovec_, Jul 25 2014

%t Table[n! * (n-8)^2*(n-7)^2*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(9*n^4 - 234*n^3 + 2211*n^2 - 8938*n + 12960)/234101145600,{n,9,20}] (* _Vaclav Kotesovec_, Jul 25 2014 *)

%o (Magma) [Factorial(n)*(n-8)^2*(n-7)^2*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(9*n^4 - 234*n^3 + 2211*n^2 - 8938*n + 12960)/234101145600 : n in [9..25]]; // _Vincenzo Librandi_, Jul 25 2014

%Y Column 8 of A055302.

%K nonn

%O 9,1

%A _Christian G. Bower_, May 11 2000