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A071208
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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 number k of decreasing edges.
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0
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1, 2, 2, 6, 15, 6, 24, 104, 104, 24, 120, 770, 1345, 770, 120, 720, 6264, 16344, 16344, 6264, 720, 5040, 56196, 200452, 300167, 200452, 56196, 5040, 40320, 554112, 2552192, 5241984, 5241984, 2552192, 554112, 40320, 362880, 5973264, 34138908
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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REFERENCES
| 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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MAPLE
| (n, k) -> sum((-1)^(m+k+1)*binomial(m, k+1)*(-1)^(m)*stirling1(n+1, n+1-m)*n^(n-m), m=k+1..n)
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CROSSREFS
| Cf. A000312.
Sequence in context: A014431 A201687 A142471 * A083555 A001464 A067136
Adjacent sequences: A071205 A071206 A071207 * A071209 A071210 A071211
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Cedric Chauve (chauve(AT)lacim.uqam.ca), May 16 2002
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