%I #21 May 26 2024 13:25:03

%S 11,67452,48907716,14690700024,2705763420360,365758901988480,

%T 40063975278687360,3778762636904935680,319426407028867057920,

%U 24881574582258352358400,1822046744492620226380800

%N Number of labeled trees with n nodes and 10 leaves.

%H Vincenzo Librandi, <a href="/A055322/b055322.txt">Table of n, a(n) for n = 11..200</a>

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

%F a(n) = (n!/10!)*Stirling2(n-2, n-10). - _Vladeta Jovovic_, Jan 28 2004

%F a(n) = n! * (n-10)*(n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(135*n^7 - 8190*n^6 + 211050*n^5 - 2991660*n^4 + 25164055*n^3 - 125425110*n^2 + 342426104*n - 394205184) / 5056584744960000. - _Vaclav Kotesovec_, Jul 25 2014

%t Table[n! * (n-10)*(n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(135*n^7 - 8190*n^6 + 211050*n^5 - 2991660*n^4 + 25164055*n^3 - 125425110*n^2 + 342426104*n - 394205184) / 5056584744960000,{n,11,25}] (* _Vaclav Kotesovec_, Jul 25 2014 *)

%o (Magma) [Factorial(n)*(n-10)*(n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(135*n^7 - 8190*n^6 + 211050*n^5 - 2991660*n^4 + 25164055*n^3 - 125425110*n^2 + 342426104*n - 394205184) / 5056584744960000: n in [11..25]]; // _Vincenzo Librandi_, Jul 25 2014

%Y Column 10 of A055314.

%K nonn

%O 11,1

%A _Christian G. Bower_, May 11 2000