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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.

%I A106238 #23 Jan 14 2022 23:19:24
%S A106238 1,1,1,5,1,1,83,6,1,1,5048,88,6,1,1,1047008,5146,89,6,1,1,705422362,
%T A106238 1052471,5151,89,6,1,1,1580348371788,706498096,1052569,5152,89,6,1,1,
%U A106238 12139024825260556,1581059448174,706503594,1052574,5152,89,6,1,1
%N A106238 Triangle read by rows: T(n,m) is the number of semi-strong digraphs on n unlabeled nodes with m connected components.
%C A106238 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.)
%C A106238 A digraph is semi-strong if all its weakly connected components are strongly connected. - _Andrew Howroyd_, Jan 14 2022
%H A106238 Andrew Howroyd, <a href="/A106238/b106238.txt">Table of n, a(n) for n = 1..1275</a> (rows 1..50)
%F A106238 G.f.: 1/Product_{i>=1} (1-y*x^i)^A035512(i). - _Vladeta Jovovic_, May 04 2005
%F A106238 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).
%e A106238 Triangle begins:
%e A106238           1;
%e A106238           1,       1;
%e A106238           5,       1,    1;
%e A106238          83,       6,    1,  1;
%e A106238        5048,      88,    6,  1, 1;
%e A106238     1047008,    5146,   89,  6, 1, 1;
%e A106238   705422362, 1052471, 5151, 89, 6, 1, 1;
%e A106238   ...
%e A106238 T(4,2) = 6 because there are 6 digraphs of order 4 with 2 strongly connected components.
%Y A106238 Row sums are A350754.
%Y A106238 Column 1 is A035512.
%Y A106238 Cf. A057276, A106237, A106239.
%K A106238 nonn,tabl
%O A106238 1,4
%A A106238 _Washington Bomfim_, May 01 2005
%E A106238 Definition clarified by _Andrew Howroyd_, Jan 14 2022