A055324 Number of labeled trees with n nodes and 12 leaves.
13, 372554, 714236250, 453911421600, 156507084115200, 36555247168352640, 6528715119143118720, 960135043767367104000, 122086105154945279712000, 13885903109630633425344000, 1447862009053077400092710400, 140958354488116955062668595200
Offset: 13
Keywords
Links
- Vincenzo Librandi, Table of n, a(n) for n = 13..200
- Index entries for sequences related to trees
Crossrefs
Column 12 of A055314.
Programs
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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
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Magma
[(Factorial(n)/Factorial(12))*StirlingSecond(n-2, n-12): n in [13..30]]; // G. C. Greubel, Feb 07 2018
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Mathematica
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 *) Table[(n!/12!)*StirlingS2[n-2, n-12], {n,13, 30}] (* G. C. Greubel, Feb 07 2018 *) -
PARI
for(n=13, 30, print1((n!/12!)*stirling(n-2, n-12, 2), ", ")) \\ G. C. Greubel, Feb 07 2018
Formula
a(n) = (n!/12!)*Stirling2(n-2, n-12). - Vladeta Jovovic, Jan 28 2004
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
Extensions
Missing a(24) inserted by Andrew Howroyd, Feb 23 2018