A055306 - OEIS

%I #16 Sep 08 2022 08:45:01

%S 6,1302,101136,5143824,210198240,7593173280,255415628160,

%T 8252203639680,261173083691520,8202954132172800,257956727815987200,

%U 8172268419809894400,261973287647034163200,8524055367713146060800

%N Number of labeled rooted trees with n nodes and 5 leaves.

%H Vincenzo Librandi, <a href="/A055306/b055306.txt">Table of n, a(n) for n = 6..200</a>

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

%F a(n) = n! * (n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(15*n^3 - 195*n^2 + 830*n - 1152)/691200. - _Vaclav Kotesovec_, Jul 25 2014

%F E.g.f: x^6*(1+22*x+58*x^2+24*x^3)/(120*(1-x)^9). - _Robert Israel_, Jul 25 2014

%t Table[n! * (n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(15*n^3 - 195*n^2 + 830*n - 1152)/691200,{n,6,20}] (* _Vaclav Kotesovec_, Jul 25 2014 *)

%o (Magma) [Factorial(n)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(15*n^3 - 195*n^2 + 830*n - 1152)/691200 : n in [6..25]]; // _Vincenzo Librandi_, Jul 25 2014

%Y Column 5 of A055302.

%K nonn

%O 6,1

%A _Christian G. Bower_, May 11 2000