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A088326
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Triangle T(n,k) (n>=1, 1<=k<=n) read by rows, giving number of Piet Hut's "coat-hanger" arrangements: unlabeled forests of rooted trees with n edges and k connected components, in which the outdegree of each node is <= 2 and the symmetric group acts on the components.
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1
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1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 6, 5, 3, 1, 1, 11, 12, 6, 3, 1, 1, 23, 23, 14, 6, 3, 1, 1, 46, 52, 29, 15, 6, 3, 1, 1, 98, 109, 68, 31, 15, 6, 3, 1, 1, 207, 244, 147, 74, 32, 15, 6, 3, 1, 1, 451, 532, 337, 163, 76, 32, 15, 6, 3, 1, 1, 983, 1196, 757, 380, 169, 77, 32, 15, 6, 3, 1, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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FORMULA
| G.f.: exp(sum_{k=1..infinity) z^k*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.
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EXAMPLE
| See A088325 for illustration.
Triangle begins
1
1 1
2 1 1
3 3 1 1
6 5 3 1 1
11 12 6 3 1 1
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CROSSREFS
| First 3 columns are A001190, A036657, A036658. Row sums are A088325.
Sequence in context: A034364 A090011 A061554 * A181039 A124975 A171246
Adjacent sequences: A088323 A088324 A088325 * A088327 A088328 A088329
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 06 2003
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 06 2003
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