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A088325
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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.
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4
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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
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0,3
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COMMENTS
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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.
Arises when studying number of different configurations possible in a multiple star system.
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LINKS
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Table of n, a(n) for n=0..33.
Piet Hut, Home Page
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FORMULA
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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.
G.f.: 1/Product_{k>0} (1-x^k)^A001190(k+1). - Vladeta Jovovic, May 29 2005
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EXAMPLE
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The eight possibilities with 4 edges are:
.||||..|||..|.|..||..||...|....|...|.
.......|.../.\...|...||../.\...|...|.
.................|.......|..../.\..|.
...................................|.
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CROSSREFS
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Cf. A001190, A003214. Row sums of A088326.
Sequence in context: A084636 A161869 A210541 * A215930 A006210 A096812
Adjacent sequences: A088322 A088323 A088324 * A088326 A088327 A088328
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Nov 06 2003
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STATUS
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approved
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