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.

1, 0, 1, 0, 1, 2, 0, 18, 18, 18, 0, 1606, 1098, 684, 446, 0, 565080, 263580, 116370, 55620, 26430, 0, 734774776, 225806940, 68822910, 24578010, 9729090, 3596762, 0, 3523091615568, 680637057912, 136498491360, 34626926250, 10819771830, 3694824126, 1111506858

Offset: 0

Author

Andrew Howroyd, May 04 2023

Keywords

• nonn
• tabl

Examples

			Triangle begins:
  1;
  0,         1;
  0,         1,         2;
  0,        18,        18,       18;
  0,      1606,      1098,      684,      446;
  0,    565080,    263580,   116370,    55620,   26430;
  0, 734774776, 225806940, 68822910, 24578010, 9729090, 3596762;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50).

Crossrefs

Column k=1 is A003030.

Main diagonal is A082402.

Row sums are A003027.

The unlabeled version is A361587.

Cf. A189898, A361455.

Programs

PARI

\\ Uses functions defined in A361455.
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))))))))))]}
{ my(A=T(6)); for(i=1, #A, print(A[i])) }