|
|
A005173
|
|
Number of trees of subsets of an n-set.
(Formerly M4844)
|
|
2
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
More terms from Larry Reeves (larryr(AT)acm.org), Feb 06 2001
|
|
STATUS
|
approved
|
|
|
|