%I #23 Sep 08 2022 08:45:01

%S 13,372554,714236250,453911421600,156507084115200,36555247168352640,

%T 6528715119143118720,960135043767367104000,122086105154945279712000,

%U 13885903109630633425344000,1447862009053077400092710400,140958354488116955062668595200

%N Number of labeled trees with n nodes and 12 leaves.

%H Vincenzo Librandi, <a href="/A055324/b055324.txt">Table of n, a(n) for n = 13..200</a>

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

%F a(n) = (n!/12!)*Stirling2(n-2, n-12). - _Vladeta Jovovic_, Jan 28 2004

%F a(n) = n! * (n-12)*(n-11)*(n-10)*(n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(99*n^9 - 9207*n^8 + 377586*n^7 - 8955870*n^6 + 135276603*n^5 - 1348112183*n^4 + 8853485696*n^3 - 36897359092*n^2 + 88399944688*n - 92577669120) / 176211865192366080000. - _Vaclav Kotesovec_, Jul 25 2014

%t Table[n! * (n-12)*(n-11)*(n-10)*(n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(99*n^9 - 9207*n^8 + 377586*n^7 - 8955870*n^6 + 135276603*n^5 - 1348112183*n^4 + 8853485696*n^3 - 36897359092*n^2 + 88399944688*n - 92577669120) / 176211865192366080000,{n,13,25}] (* _Vaclav Kotesovec_, Jul 25 2014 *)

%t Table[(n!/12!)*StirlingS2[n-2, n-12], {n,13, 30}] (* _G. C. Greubel_, Feb 07 2018 *)

%o (Magma) [Factorial(n)*(n-12)*(n-11)*(n-10)*(n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(99*n^9 - 9207*n^8 + 377586*n^7 - 8955870*n^6 + 135276603*n^5 - 1348112183*n^4 + 8853485696*n^3 - 36897359092*n^2 + 88399944688*n - 92577669120) / 176211865192366080000: n in [13..25]]; // _Vincenzo Librandi_, Jul 25 2014

%o (PARI) for(n=13, 30, print1((n!/12!)*stirling(n-2, n-12, 2), ", ")) \\ _G. C. Greubel_, Feb 07 2018

%o (Magma) [(Factorial(n)/Factorial(12))*StirlingSecond(n-2, n-12): n in [13..30]]; // _G. C. Greubel_, Feb 07 2018

%Y Column 12 of A055314.

%K nonn

%O 13,1

%A _Christian G. Bower_, May 11 2000

%E Missing a(24) inserted by _Andrew Howroyd_, Feb 23 2018