cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A055321 #29 Sep 08 2022 08:45:01
%S A055321 10,28050,12315600,2501070000,331387056000,33590279923200,
%T A055321 2844207894528000,212334102908928000,14481281691676800000,
%U A055321 924652322084050560000,56256869188969473024000,3303981073122303974400000,189156797595688810567680000,10636600593905858347776000000
%N A055321 Number of labeled trees with n nodes and 9 leaves.
%H A055321 Vincenzo Librandi, <a href="/A055321/b055321.txt">Table of n, a(n) for n = 10..200</a>
%H A055321 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A055321 a(n) = (n!/9!)*Stirling2(n-2, n-9). - _Vladeta Jovovic_, Jan 28 2004
%F A055321 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 A055321 a:= n-> (n!/9!)*Stirling2(n-2, n-9):
%p A055321 seq(a(n), n=10..25);  # _Alois P. Heinz_, Mar 06 2012
%t A055321 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 A055321 (Maxima) A055321(n) := block(
%o A055321         A055314(n,9)
%o A055321 )$
%o A055321 for n : 10 thru 25 do
%o A055321         print(A055321(n)," ") ; /* _R. J. Mathar_, Mar 06 2012 */
%o A055321 (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 A055321 (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 A055321 Column 9 of A055314.
%K A055321 nonn
%O A055321 10,1
%A A055321 _Christian G. Bower_, May 11 2000