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Search: id:A005175
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| A005175 |
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Number of trees of subsets of an n-set.
(Formerly M3173)
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+0
1
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| 0, 0, 3, 131, 1830, 16990, 127953, 851361, 5231460, 30459980, 170761503, 931484191, 4979773890, 26223530970, 136522672653, 704553794621, 3611494269120, 18415268221960, 93516225653403, 473366777478651
(list; graph; listen)
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OFFSET
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1,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
F. R. McMorris and T. Zaslavsky, The number of cladistic characters, Math. Biosciences, 54 (1981), 3-10.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index entries for sequences related to trees
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FORMULA
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3*(3^n-2*2^n+1)/2 + 113*(4^n-3*3^n+3*2^n-1)/6 + 625*(5^n-4*4^n+6*3^n-4*2^n+1)/24 - formula fitted by John Layman (layman(AT)calvin.math.vt.edu).
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MAPLE
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A005175:=-z**2*(3+86*z+120*z**2)/(z-1)/(4*z-1)/(3*z-1)/(2*z-1)/(5*z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Sequence in context: A003370 A156957 A139943 this_sequence A082439 A082622 A075597
Adjacent sequences: A005172 A005173 A005174 this_sequence A005176 A005177 A005178
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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