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Triangle read by rows: T(n,k) is the number of weakly connected simple digraphs on n labeled nodes with k strongly connected components.
2

%I #6 May 04 2023 14:57:38

%S 1,0,1,0,1,2,0,18,18,18,0,1606,1098,684,446,0,565080,263580,116370,

%T 55620,26430,0,734774776,225806940,68822910,24578010,9729090,3596762,

%U 0,3523091615568,680637057912,136498491360,34626926250,10819771830,3694824126,1111506858

%N Triangle read by rows: T(n,k) is the number of weakly connected simple digraphs on n labeled nodes with k strongly connected components.

%H Andrew Howroyd, <a href="/A361591/b361591.txt">Table of n, a(n) for n = 0..1325</a> (rows 0..50).

%e Triangle begins:

%e 1;

%e 0, 1;

%e 0, 1, 2;

%e 0, 18, 18, 18;

%e 0, 1606, 1098, 684, 446;

%e 0, 565080, 263580, 116370, 55620, 26430;

%e 0, 734774776, 225806940, 68822910, 24578010, 9729090, 3596762;

%e ...

%o (PARI) \\ Uses functions defined in A361455.

%o T(n)={my(e=2); [Vecrev(p) | p<-Vec(serlaplace(1 + log(U(e, 1/G(e, exp(y*log(U(e, 1/G(e, DigraphEgf(n, e))))))))))]}

%o { my(A=T(6)); for(i=1, #A, print(A[i])) }

%Y Column k=1 is A003030.

%Y Main diagonal is A082402.

%Y Row sums are A003027.

%Y The unlabeled version is A361587.

%Y Cf. A189898, A361455.

%K nonn,tabl

%O 0,6

%A _Andrew Howroyd_, May 04 2023