login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A055321 Number of labeled trees with n nodes and 9 leaves. 1

%I #29 Sep 08 2022 08:45:01

%S 10,28050,12315600,2501070000,331387056000,33590279923200,

%T 2844207894528000,212334102908928000,14481281691676800000,

%U 924652322084050560000,56256869188969473024000,3303981073122303974400000,189156797595688810567680000,10636600593905858347776000000

%N Number of labeled trees with n nodes and 9 leaves.

%H Vincenzo Librandi, <a href="/A055321/b055321.txt">Table of n, a(n) for n = 10..200</a>

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

%F a(n) = (n!/9!)*Stirling2(n-2, n-9). - _Vladeta Jovovic_, Jan 28 2004

%F 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

%p a:= n-> (n!/9!)*Stirling2(n-2, n-9):

%p seq(a(n), n=10..25); # _Alois P. Heinz_, Mar 06 2012

%t 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 *)

%o (Maxima) A055321(n) := block(

%o A055314(n,9)

%o )$

%o for n : 10 thru 25 do

%o print(A055321(n)," ") ; /* _R. J. Mathar_, Mar 06 2012 */

%o (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 */

%o (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

%Y Column 9 of A055314.

%K nonn

%O 10,1

%A _Christian G. Bower_, May 11 2000

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)