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%I M4844 #34 Oct 27 2023 09:06:23
%S 0,1,12,61,240,841,2772,8821,27480,84481,257532,780781,2358720,
%T 7108921,21392292,64307941,193185960,580082161,1741295052,5225982301,
%U 15682141200,47054812201,141181213812,423577195861,1270798696440
%N Number of trees of subsets of an n-set.
%D F. R. McMorris and T. Zaslavsky, The number of cladistic characters, Math. Biosciences, 54 (1981), 3-10.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H F. R. McMorris and T. Zaslavsky, <a href="/A005172/a005172.pdf">The number of cladistic characters</a>, Math. Biosciences, 54 (1981), 3-10. [Annotated scanned copy]
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992.
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6, -11, 6).
%F G.f.: x*(1 + 6*x) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). [corrected by _Ray Chandler_, Jun 26 2023]
%F First differences give A003063, 3^(n-1) - 2^n.
%p A005173:=-z*(1+6*z)/(z-1)/(3*z-1)/(2*z-1); # conjectured by _Simon Plouffe_ in his 1992 dissertation
%t CoefficientList[Series[x (1+6 x)/(1-x)/(1-2 x)/(1-3 x),{x,0,30}],x] (* _Harvey P. Dale_, Jul 03 2023 *)
%Y Cf. A003063.
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_
%E More terms from Larry Reeves (larryr(AT)acm.org), Feb 06 2001
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