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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.
Sequence in context: A246051 A111820 A174912 * A173475 A174919 A156952
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.)