

A106238


Triangle read by rows: T(n,m) is the number of semistrong 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
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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 nonisomorphic connected components of order i. (In general, f denotes a sequence that counts unlabeled connected combinatorial objects.)
A digraph is semistrong if all its weakly connected components are strongly connected.  Andrew Howroyd, Jan 14 2022


LINKS



FORMULA

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.


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STATUS

approved



