A055321 Number of labeled trees with n nodes and 9 leaves.

10, 28050, 12315600, 2501070000, 331387056000, 33590279923200, 2844207894528000, 212334102908928000, 14481281691676800000, 924652322084050560000, 56256869188969473024000, 3303981073122303974400000, 189156797595688810567680000, 10636600593905858347776000000

Offset: 10

Author

Christian G. Bower, May 11 2000

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 10..200
• Index entries for sequences related to trees

Crossrefs

Column 9 of A055314.

Programs

Magma

[Factorial(n)*(n-9)^2*(n-8)^2*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(9*n^4 - 270*n^3 + 2967*n^2 - 14098*n + 24352)/2106910310400: n in [10..25]]; // Vincenzo Librandi, Jul 25 2014

Maple

a:= n-> (n!/9!)*Stirling2(n-2, n-9):
seq(a(n), n=10..25);  # Alois P. Heinz, Mar 06 2012

Mathematica

Table[n! * (n-9)^2*(n-8)^2*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(9*n^4 - 270*n^3 + 2967*n^2 - 14098*n + 24352)/2106910310400,{n,10,25}] (* Vaclav Kotesovec, Jul 25 2014 *)

Maxima

A055321(n) := block(
        A055314(n,9)
)$
for n : 10 thru 25 do
        print(A055321(n)," ") ; /* R. J. Mathar, Mar 06 2012 */

PARI

A055321(n)={binomial(n,9)*sum(i=0,n-=9,(-1)^i*binomial(n,i)*i^(n+7))*(-1)^n} /* or: Stirling2(n-2, n-9)*n!/9!, cf. A008277 */ /* M. F. Hasler, Mar 06 2012 */

Formula

a(n) = (n!/9!)*Stirling2(n-2, n-9). - Vladeta Jovovic, Jan 28 2004

a(n) = n! * (n-9)^2*(n-8)^2*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(9*n^4 - 270*n^3 + 2967*n^2 - 14098*n + 24352)/2106910310400. - Vaclav Kotesovec, Jul 25 2014