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 A106238 Triangle read by rows: T(n,m) is the number of semi-strong digraphs on n unlabeled nodes with m connected components. 4
 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; text; internal format)
 OFFSET 1,4 COMMENTS The formula T(n,m) is the sum over the partitions of n with m parts 1K1 + 2K2 + ... + nKn, of Product_{i=1..n} binomial(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.) A digraph is semi-strong if all its weakly connected components are strongly connected. - Andrew Howroyd, Jan 14 2022 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1275 (rows 1..50) FORMULA G.f.: 1/Product_{i>=1} (1-y*x^i)^A035512(i). - Vladeta Jovovic, May 04 2005 Triangle read by rows: T(n, m) is the sum over the partitions of n with m parts 1K1 + 2K2 + ... + nKn, of Product_{i=1..n} binomial(A035512(i) + Ki - 1, Ki). EXAMPLE Triangle begins: 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; ... T(4,2) = 6 because there are 6 digraphs of order 4 with 2 strongly connected components. CROSSREFS Row sums are A350754. Column 1 is A035512. Cf. A057276, A106237, A106239. Sequence in context: A246051 A111820 A174912 * A173475 A174919 A156952 Adjacent sequences: A106235 A106236 A106237 * A106239 A106240 A106241 KEYWORD nonn,tabl AUTHOR Washington Bomfim, May 01 2005 EXTENSIONS Definition clarified by Andrew Howroyd, Jan 14 2022 STATUS approved

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Last modified May 27 23:16 EDT 2024. Contains 372900 sequences. (Running on oeis4.)