A055306 Number of labeled rooted trees with n nodes and 5 leaves.

6, 1302, 101136, 5143824, 210198240, 7593173280, 255415628160, 8252203639680, 261173083691520, 8202954132172800, 257956727815987200, 8172268419809894400, 261973287647034163200, 8524055367713146060800

Offset: 6

Author

Christian G. Bower, May 11 2000

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 6..200
• Index entries for sequences related to rooted trees

Crossrefs

Column 5 of A055302.

Programs

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

Mathematica

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 *)

Formula

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

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