%I #23 Sep 08 2022 08:45:01
%S 4,140,3000,54600,940800,16087680,279417600,4989600000,92207808000,
%T 1769511744000,35321737651200,733823266176000,15866448998400000,
%U 356873052856320000,8344427063132160000,202660737281114112000
%N Number of labeled rooted trees with n nodes and 3 leaves.
%H Vincenzo Librandi, <a href="/A055304/b055304.txt">Table of n, a(n) for n = 4..200</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F a(n) = (n!/3!)*Stirling2(n-1, n-3). - _Vladeta Jovovic_, Jan 28 2004
%F a(n) = n! * (n-3)*(n-2)*(n-1)*(3*n-8)/144. - _Vaclav Kotesovec_, Jul 25 2014
%F E.g.f.: x^4*(2*x+1)/(6*(1-x)^5). - _Robert Israel_, Jul 25 2014
%p seq(n!*(n-3)*(n-2)*(n-1)*(3*n-8)/144, n=4..100); # _Robert Israel_, Jul 25 2014
%t Table[n! * (n-3)*(n-2)*(n-1)*(3*n-8)/144,{n,4,20}] (* _Vaclav Kotesovec_, Jul 25 2014 *)
%o (Magma) [Factorial(n)*(n-3)*(n-2)*(n-1)*(3*n-8)/144 : n in [4..25]]; // _Vincenzo Librandi_, Jul 25 2014
%Y Column 3 of A055302.
%K nonn
%O 4,1
%A _Christian G. Bower_, May 11 2000