%I A088325
%S A088325 1,1,2,4,8,16,34,71,153,332,730,1617,3620,8148,18473,42097,96420,221770,
%T A088325 512133,1186712,2758707,6431395,15033320,35224825,82720273,194655030,458931973,
%U A088325 1083926784,2564305754,6075896220,14417163975,34256236039,81499535281,
               194130771581
%N A088325 Piet Hut's "coat-hanger" 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.
%C A088325 The coat-hangers hang on a single rod and each coat-hanger may have 0, 
               1 or 2 coat-hangers hanging from it. There are n coat-hangers.
%C A088325 Arises when studying number of different configurations possible in a 
               multiple star system.
%H A088325 Piet Hut, <a href="http://www.sns.ias.edu/~piet/">Home Page</a>
%F A088325 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 Wedderburn-Etherington numbers A001190. - N. J. 
               A. Sloane (njas(AT)research.att.com).
%F A088325 G.f.: 1/Product_{k>0} (1-x^k)^A001190(k+1). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               May 29 2005
%e A088325 The eight possibilities with 4 edges are:
%e A088325 .||||..|||..|.|..||..||...|....|...|.
%e A088325 .......|.../.\...|...||../.\...|...|.
%e A088325 .................|.......|..../.\..|.
%e A088325 ...................................|.
%Y A088325 Cf. A001190, A003214. Row sums of A088326.
%Y A088325 Sequence in context: A110334 A084636 A161869 this_sequence A006210 A096812 
               A006981
%Y A088325 Adjacent sequences: A088322 A088323 A088324 this_sequence A088326 A088327 
               A088328
%K A088325 nonn
%O A088325 0,3
%A A088325 N. J. A. Sloane (njas(AT)research.att.com), Nov 06 2003