A055315 Number of labeled trees with n nodes and 3 leaves.

4, 60, 720, 8400, 100800, 1270080, 16934400, 239500800, 3592512000, 57081024000, 958961203200, 16999766784000, 317328979968000, 6224529991680000, 128047474114560000, 2757288942600192000, 62039001208504320000, 1456091851893719040000, 35593356379624243200000

Offset: 4

Author

Christian G. Bower, May 11 2000

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 4..200
• Index entries for sequences related to trees

Crossrefs

Column 3 of A055314.

Programs

Magma

[Factorial(n)*(n-3)*(n-2)/12: n in [4..25]]; // Vincenzo Librandi, Jul 25 2014

Maple

a:=n->sum((n-j)*n!/3!, j=3..n): seq(a(n), n=4..19); # Zerinvary Lajos, Apr 29 2007

Mathematica

Table[n!*(n-3)*(n-2)/12,{n,4,20}] (* Vaclav Kotesovec, Jul 25 2014 *)

PARI

for(n=4,30, print1(n!*(n-3)*(n-2)/12, ", ")) \\ G. C. Greubel, Feb 07 2018

Formula

a(n) = (n!/3!)*stirling2(n-2, n-3). - Vladeta Jovovic, Jan 28 2004

a(n) = n! * (n-3)*(n-2)/12. - Vaclav Kotesovec, Jul 25 2014

E.g.f.: x*(x/(1-x))^3/3! - Geoffrey Critzer, Sep 19 2017