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A033185
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Rooted tree triangle read by rows: a(n,k) = number of forests with n nodes and k rooted trees.
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9
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1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 9, 6, 3, 1, 1, 20, 16, 7, 3, 1, 1, 48, 37, 18, 7, 3, 1, 1, 115, 96, 44, 19, 7, 3, 1, 1, 286, 239, 117, 46, 19, 7, 3, 1, 1, 719, 622, 299, 124, 47, 19, 7, 3, 1, 1, 1842, 1607, 793, 320, 126, 47, 19, 7, 3, 1, 1, 4766, 4235, 2095, 858, 327, 127, 47
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Leading column: A000081, rows sums: A000081 shifted.
Also, number of multigraphs of k components, n nodes, and no cycles except one loop in each component. See link below to have a picture showing the bijection between rooted forests and multigraphs of this kind. [From W. Bomfim (webonfim(AT)bol.com.br), Sep 04 2010]
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LINKS
| W. Bomfim, Bijection between rooted forests and multigraphs without cycles except one loop in each connected component. [From W. Bomfim (webonfim(AT)bol.com.br), Sep 04 2010]
Index entries for sequences related to rooted trees
Index entries for sequences related to trees
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FORMULA
| G.f.: 1/Product((1-x*y^i)^A000081(i), i=1..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 28 2005
a(n, k)= sum over the partitions of n, 1M1+2M2+...+nMn, with exactly k parts, of product_{1=<i<=n}C(A000081(i)+Mi-1, Mi). - Washington Bomfim (webonfim(AT)bol.com.br), May 12 2005
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EXAMPLE
| Triangle begins:
1,
1, 1,
2, 1, 1,
4, 3, 1, 1,
9, 6, 3, 1, 1,
20, 16, 7, 3, 1, 1,
48, 37, 18, 7, 3, 1, 1,
115, 96, 44, 19, 7, 3, 1, 1,
286, 239, 117, 46, 19, 7, 3, 1, 1,
719, 622, 299, 124, 47, 19, 7, 3, 1, 1, 1
842, 1607, 793, 320, 126, 47, 19, 7, 3, 1, 1,
...
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CROSSREFS
| Cf. A000081, A106240, A181360.
Sequence in context: A092056 A103574 A112682 * A204849 A105632 A091491
Adjacent sequences: A033182 A033183 A033184 * A033186 A033187 A033188
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KEYWORD
| nonn,tabl
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net)
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