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%I #20 Sep 08 2022 08:45:01
%S 7,3528,486864,39160800,2357586000,119409111360,5426122141440,
%T 230006844587520,9326497051872000,367969396354560000,
%U 14295131088292454400,551514022702420377600,21263333439482226892800
%N Number of labeled rooted trees with n nodes and 6 leaves.
%H Vincenzo Librandi, <a href="/A055307/b055307.txt">Table of n, a(n) for n = 7..200</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F a(n) = n! * (n-6)^2*(n-5)^2*(n-4)*(n-3)*(n-2)*(n-1)*(3*n^2 - 29*n + 64)/8294400. - _Vaclav Kotesovec_, Jul 25 2014
%F E.g.f: x^7*(120*x^4+444*x^3+328*x^2+52*x+1)/(720*(1-x)^11). - _Robert Israel_, Jul 25 2014
%p seq(n! * (n-6)^2*(n-5)^2*(n-4)*(n-3)*(n-2)*(n-1)*(3*n^2 - 29*n + 64)/8294400, n=7..100); # _Robert Israel_, Jul 25 2014
%t Table[n! * (n-6)^2*(n-5)^2*(n-4)*(n-3)*(n-2)*(n-1)*(3*n^2 - 29*n + 64)/8294400,{n,7,20}] (* _Vaclav Kotesovec_, Jul 25 2014 *)
%o (Magma) [Factorial(n)*(n-6)^2*(n-5)^2*(n-4)*(n-3)*(n-2)*(n-1)*(3*n^2-29*n+ 64)/8294400: n in [7..25]]; // _Vincenzo Librandi_, Jul 25 2014
%Y Column 6 of A055302.
%K nonn
%O 7,1
%A _Christian G. Bower_, May 11 2000
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