%I #15 Sep 08 2022 08:45:01
%S 13,745290,2153888100,1850107896000,813987254808000,
%T 233983253596659840,50146687652338368000,8684014103185704192000,
%U 1281139242561407305440000,167044094432657294973120000
%N Number of labeled rooted trees with n nodes and 12 leaves.
%H Vincenzo Librandi, <a href="/A055313/b055313.txt">Table of n, a(n) for n = 13..200</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F a(n) = n! * (n-12)^2*(n-11)^2*(n-10)*(n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(9*n^8 - 708*n^7 + 24018*n^6 - 458136*n^5 + 5363513*n^4 - 39369364*n^3 + 176423596*n^2 - 439700816*n + 464486400) / 352423730384732160000. - _Vaclav Kotesovec_, Jul 25 2014
%t Table[n! * (n-12)^2*(n-11)^2*(n-10)*(n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(9*n^8 - 708*n^7 + 24018*n^6 - 458136*n^5 + 5363513*n^4 - 39369364*n^3 + 176423596*n^2 - 439700816*n + 464486400) / 352423730384732160000,{n,13,25}] (* _Vaclav Kotesovec_, Jul 25 2014 *)
%o (Magma) [Factorial(n)*(n-12)^2*(n-11)^2*(n-10)*(n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(9*n^8 - 708*n^7 + 24018*n^6 - 458136*n^5 + 5363513*n^4 - 39369364*n^3 + 176423596*n^2 - 439700816*n + 464486400) / 352423730384732160000: n in [13..25]]; // _Vincenzo Librandi_, Jul 25 2014
%Y Column 12 of A055302.
%K nonn
%O 13,1
%A _Christian G. Bower_, May 11 2000