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 A005175 Number of trees of subsets of an n-set. (Formerly M3173) 1
 0, 0, 3, 131, 1830, 16990, 127953, 851361, 5231460, 30459980, 170761503, 931484191, 4979773890, 26223530970, 136522672653, 704553794621, 3611494269120, 18415268221960, 93516225653403, 473366777478651, 2390054857197150, 12043393363764950, 60590148885015753 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS F. R. McMorris and T. Zaslavsky, The number of cladistic characters, Math. Biosciences, 54 (1981), 3-10. F. R. McMorris and T. Zaslavsky, The number of cladistic characters, Math. Biosciences, 54 (1981), 3-10. [Annotated scanned copy] Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992. Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992 FORMULA 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 W. Layman. a(n) = (125/24) * 5^n - (64/3) * 4^n + (135/4)*3^n - (76/3) * 2^n + 209/24 proven in McMorris and Zaslavsky, matches Layman's formula with an offset of 1. - Sean A. Irvine, Apr 12 2016 E.g.f.: (1/24)*exp(x)*(-1 + exp(x))^2*(209 - 798*exp(x) + 625*exp(2*x)). - Ilya Gutkovskiy, Apr 12 2016 MAPLE 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 Simon Plouffe in his 1992 dissertation. MATHEMATICA Table[(125/24) 5^n - (64/3) 4^n + (135/4) 3^n - (76/3) 2^n + 209/24, {n, 20}] (* Michael De Vlieger, Apr 12 2016 *) CROSSREFS Sequence in context: A202030 A249379 A139943 * A082439 A082622 A332113 Adjacent sequences:  A005172 A005173 A005174 * A005176 A005177 A005178 KEYWORD nonn AUTHOR STATUS approved

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Last modified April 13 12:29 EDT 2021. Contains 342936 sequences. (Running on oeis4.)