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A005174
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Number of trees of subsets of an n-set.
(Formerly M4738)
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1
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0, 0, 10, 124, 890, 5060, 25410, 118524, 527530, 2276020, 9613010, 40001324, 164698170, 672961380, 2734531810, 11066546524, 44652164810, 179768037140, 722553165810, 2900661482124, 11634003919450, 46630112719300, 186802788139010, 748058256616124
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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).
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LINKS
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FORMULA
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The terms a(1)-a(18) are given by a(n) = (8/3)*(4^n - 4) - 9*3^n + 11*2^n + 5. - John W. Layman, Jul 20 1999
Formula of Layman matches the proven formula in McMorris and Zaslavsky. - Sean A. Irvine, Apr 12 2016
E.g.f.: (1/3)*(-17*exp(x) + 66*exp(2*x) - 81*exp(3*x) + 32*exp(4*x)). - Ilya Gutkovskiy, Apr 12 2016
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MAPLE
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A005174:=2*z**2*(5+12*z)/(z-1)/(3*z-1)/(2*z-1)/(4*z-1); # conjectured by Simon Plouffe in his 1992 dissertation
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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