A005173 Number of trees of subsets of an n-set. (Formerly M4844)

0, 1, 12, 61, 240, 841, 2772, 8821, 27480, 84481, 257532, 780781, 2358720, 7108921, 21392292, 64307941, 193185960, 580082161, 1741295052, 5225982301, 15682141200, 47054812201, 141181213812, 423577195861, 1270798696440

Offset

1,3

References

F. R. McMorris and T. Zaslavsky, The number of cladistic characters, Math. Biosciences, 54 (1981), 3-10.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..25.

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; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992.

Index entries for sequences related to trees

Index entries for linear recurrences with constant coefficients, signature (6, -11, 6).

Formula

G.f.: x*(1 + 6*x) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). [corrected by Ray Chandler, Jun 26 2023]

First differences give A003063, 3^(n-1) - 2^n.

Maple

A005173:=-z*(1+6*z)/(z-1)/(3*z-1)/(2*z-1); # conjectured by Simon Plouffe in his 1992 dissertation

Mathematica

CoefficientList[Series[x (1+6 x)/(1-x)/(1-2 x)/(1-3 x), {x, 0, 30}], x] (* Harvey P. Dale, Jul 03 2023 *)

Crossrefs

Cf. A003063.

Sequence in context: A240002 A114241 A127766 * A196144 A294682 A177677

Adjacent sequences: A005170 A005171 A005172 * A005174 A005175 A005176

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Feb 06 2001

Status

approved