A055304 Number of labeled rooted trees with n nodes and 3 leaves.

4, 140, 3000, 54600, 940800, 16087680, 279417600, 4989600000, 92207808000, 1769511744000, 35321737651200, 733823266176000, 15866448998400000, 356873052856320000, 8344427063132160000, 202660737281114112000

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 rooted trees

Crossrefs

Column 3 of A055302.

Programs

Magma

[Factorial(n)*(n-3)*(n-2)*(n-1)*(3*n-8)/144 : n in [4..25]]; // Vincenzo Librandi, Jul 25 2014

Maple

seq(n!*(n-3)*(n-2)*(n-1)*(3*n-8)/144, n=4..100); # Robert Israel, Jul 25 2014

Mathematica

Table[n! * (n-3)*(n-2)*(n-1)*(3*n-8)/144,{n,4,20}] (* Vaclav Kotesovec, Jul 25 2014 *)

Formula

a(n) = (n!/3!)*Stirling2(n-1, n-3). - Vladeta Jovovic, Jan 28 2004

a(n) = n! * (n-3)*(n-2)*(n-1)*(3*n-8)/144. - Vaclav Kotesovec, Jul 25 2014

E.g.f.: x^4*(2*x+1)/(6*(1-x)^5). - Robert Israel, Jul 25 2014