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A361591 Triangle read by rows: T(n,k) is the number of weakly connected simple digraphs on n labeled nodes with k strongly connected components.

%I A361591 #6 May 04 2023 14:57:38
%S A361591 1,0,1,0,1,2,0,18,18,18,0,1606,1098,684,446,0,565080,263580,116370,
%T A361591 55620,26430,0,734774776,225806940,68822910,24578010,9729090,3596762,
%U A361591 0,3523091615568,680637057912,136498491360,34626926250,10819771830,3694824126,1111506858
%N A361591 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 A361591 Andrew Howroyd, <a href="/A361591/b361591.txt">Table of n, a(n) for n = 0..1325</a> (rows 0..50).
%e A361591 Triangle begins:
%e A361591   1;
%e A361591   0,         1;
%e A361591   0,         1,         2;
%e A361591   0,        18,        18,       18;
%e A361591   0,      1606,      1098,      684,      446;
%e A361591   0,    565080,    263580,   116370,    55620,   26430;
%e A361591   0, 734774776, 225806940, 68822910, 24578010, 9729090, 3596762;
%e A361591   ...
%o A361591 (PARI) \\ Uses functions defined in A361455.
%o A361591 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 A361591 { my(A=T(6)); for(i=1, #A, print(A[i])) }
%Y A361591 Column k=1 is A003030.
%Y A361591 Main diagonal is A082402.
%Y A361591 Row sums are A003027.
%Y A361591 The unlabeled version is A361587.
%Y A361591 Cf. A189898, A361455.
%K A361591 nonn,tabl
%O A361591 0,6
%A A361591 _Andrew Howroyd_, May 04 2023