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A071211
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Triangular array T(n,k) read by rows, giving number of labeled free trees such that the root is smaller than all its children, with respect to the number n of vertices and to the label k of the root.
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0
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1, 3, 1, 16, 8, 3, 125, 75, 40, 16, 1296, 864, 540, 300, 125, 16807, 12005, 8232, 5292, 3024, 1296, 262144, 196608, 143360, 100352, 65856, 38416, 16807, 4782969, 3720087, 2834352, 2099520, 1492992, 995328, 589824, 262144, 100000000
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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REFERENCES
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C. Chauve, S. Dulucq and O. Guibert, Enumeration of some labeled trees, Proceedings of FPSAC/SFCA 2000 (Moscow), Springer, pp. 146-157.
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LINKS
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FORMULA
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T(n,k) = (n-k)*(n+1)^(n-k-1)*n^(k-1).
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MAPLE
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T:= (n, k)-> (n-k)*(n+1)^(n-k-1)*n^(k-1):
seq(seq(T(n, k), k=0..n-1), n=1..10);
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PROG
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(PARI) tabl(nn) = {for (n=1, nn, for (k=0, n-1, print1((n-k)*(n+1)^(n-k-1)*n^(k-1), ", "); ); print(); ); } \\ Michel Marcus, Jun 27 2013
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CROSSREFS
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KEYWORD
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AUTHOR
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Cedric Chauve (chauve(AT)lacim.uqam.ca), May 16 2002
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STATUS
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approved
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