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Search: id:A071207
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| A071207 |
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Triangular array T(n,k) read by rows, giving number of labeled free trees with n vertices and k children of the root that have a label smaller than the label of the root. |
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4
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| 1, 1, 1, 4, 4, 1, 27, 27, 9, 1, 256, 256, 96, 16, 1, 3125, 3125, 1250, 250, 25, 1, 46656, 46656, 19440, 4320, 540, 36, 1, 823543, 823543, 352947, 84035, 12005, 1029, 49, 1, 16777216, 16777216, 7340032, 1835008, 286720, 28672, 1792, 64, 1, 387420489
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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The n-th term of the n-th binomial transform of a sequence {b} is given by {d} where d(n) = sum(k=0,n,T(n,k)*b(k)) and T(n,k)=binomial(n,k)*n^(n-k); such diagonals are related to the hyperbinomial transform (A088956). - Paul D. Hanna (pauldhanna(AT)juno.com), Nov 04 2003
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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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FORMULA
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binomial(n, k)*n^(n-k)
E.g.f.: (-LambertW(-y)/y)^x/(1+LambertW(-y)). - Vladeta Jovovic (vladeta(AT)eunet.rs)
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MAPLE
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(n, k) -> binomial(n, k)*n^(n-k)
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PROGRAM
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(PARI) T(n, k)=if(k<0|k>n, 0, binomial(n, k)*n^(n-k))
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CROSSREFS
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Cf. A000312.
Cf. A089466, A088956.
Sequence in context: A098364 A116866 A126280 this_sequence A136214 A067328 A111845
Adjacent sequences: A071204 A071205 A071206 this_sequence A071208 A071209 A071210
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Cedric Chauve (chauve(AT)lacim.uqam.ca), May 16 2002
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