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A106238
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Triangle read by rows: T(n,m) = number of unlabeled digraphs of order n, n<=9, with m strongly connected components.
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2
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1, 1, 1, 5, 1, 1, 83, 6, 1, 1, 5048, 88, 6, 1, 1, 1047008, 5146, 89, 6, 1, 1, 705422362, 1052471, 5151, 89, 6, 1, 1, 1580348371788, 706498096, 1052569, 5152, 89, 6, 1, 1, 12139024825260556, 1581059448174, 706503594, 1052574, 5152, 89, 6, 1, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| The formula T(n,m) = sum over the partitions of n with m parts 1K1+2K2+ ... +nKn, of product_{1=<i<=n}C(f(i)+Ki-1, Ki) can be used to count unlabeled graphs of order n with m components if f(i) is the number of non-isomorphic connected components of order i. (In general f denotes a sequence that counts unlabeled connected combinatorial objects.)
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LINKS
| Washington Bomfim, Illustration of this sequence
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FORMULA
| G.f.: 1/Product((1-y*x^i)^A035512(i), i=1..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), May 04 2005
Triangle read by rows: T(n, m) = sum over the partitions of n with m parts 1K1+2K2+ ... +nKn, of product_{1=<i<=n}C(A035512(i)+Ki-= 1, Ki).
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EXAMPLE
| T(4,2)=6 because there are 6 digraphs of order 4 with 2 strongly connected components.
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CROSSREFS
| Cf. A057276, A035512, A106237, A106239.
Sequence in context: A156691 A111820 A174912 * A173475 A174919 A156952
Adjacent sequences: A106235 A106236 A106237 * A106239 A106240 A106241
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KEYWORD
| nonn,tabl
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AUTHOR
| Washington Bomfim (webonfim(AT)bol.com.br), May 01 2005
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