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

0,6

Links

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

Example

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;
  ...

Prog

(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])) }

Crossrefs

Column k=1 is A003030.

Main diagonal is A082402.

Row sums are A003027.

The unlabeled version is A361587.

Cf. A189898, A361455.

Sequence in context: A152154 A324665 A349036 * A261516 A009198 A209123

Adjacent sequences: A361588 A361589 A361590 * A361592 A361593 A361594

Keyword

nonn,tabl

Author

Andrew Howroyd, May 04 2023

Status

approved