

A088325


Piet Hut's "coathanger" sequence: unlabeled forests of rooted trees with n edges, where there can be any number of components, the outdegree of each node is <= 2 and the symmetric group acts on the components.


4



1, 1, 2, 4, 8, 16, 34, 71, 153, 332, 730, 1617, 3620, 8148, 18473, 42097, 96420, 221770, 512133, 1186712, 2758707, 6431395, 15033320, 35224825, 82720273, 194655030, 458931973, 1083926784, 2564305754, 6075896220, 14417163975, 34256236039, 81499535281, 194130771581
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OFFSET

0,3


COMMENTS

The coathangers hang on a single rod and each coathanger may have 0, 1 or 2 coathangers hanging from it. There are n coathangers.
Arises when studying number of different configurations possible in a multiple star system.


LINKS

Table of n, a(n) for n=0..33.
Piet Hut, Home Page


FORMULA

G.f.: exp(sum_{k=1..infinity) B(x^k)/k ), where B(x) = x + x^2 + 2*x^3 + 3*x^4 + 6*x^5 + 11*x^6 + ... = G001190(x)/x  1 and G001190 is the g.f. for the WedderburnEtherington numbers A001190.  N. J. A. Sloane.
G.f.: 1/Product_{k>0} (1x^k)^A001190(k+1).  Vladeta Jovovic, May 29 2005


EXAMPLE

The eight possibilities with 4 edges are:
.....................
........../.\......../.\.......
............................/.\...
....................................


CROSSREFS

Cf. A001190, A003214. Row sums of A088326.
Sequence in context: A084636 A161869 A210541 * A215930 A006210 A096812
Adjacent sequences: A088322 A088323 A088324 * A088326 A088327 A088328


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Nov 06 2003


STATUS

approved



