A361455 Triangle read by rows: T(n,k) is the number of simple digraphs on labeled n nodes with k strongly connected components.

1, 0, 1, 0, 1, 3, 0, 18, 21, 25, 0, 1606, 1173, 774, 543, 0, 565080, 271790, 122595, 59830, 29281, 0, 734774776, 229224750, 70500705, 25349355, 10110735, 3781503, 0, 3523091615568, 685793359804, 138122171880, 35130437825, 11002159455, 3767987307, 1138779265

Offset

0,6

Links

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

Formula

T(n,k) = A361269(n,k)/2^n.

Example

Triangle begins:
  1;
  0,         1;
  0,         1,         3;
  0,        18,        21,       25;
  0,      1606,      1173,      774,      543;
  0,    565080,    271790,   122595,    59830,    29281;
  0, 734774776, 229224750, 70500705, 25349355, 10110735, 3781503;
  ...

Prog

(PARI)
Z(p, f)={my(n=serprec(p, x)); serconvol(p, sum(k=0, n-1, x^k*f(k), O(x^n)))}
G(e, p)={Z(p, k->1/e^(k*(k-1)/2))}
U(e, p)={Z(p, k->e^(k*(k-1)/2))}
DigraphEgf(n, e)={sum(k=0, n, e^(k*(k-1))*x^k/k!, O(x*x^n) )}
T(n)={my(e=2); [Vecrev(p) | p<-Vec(serlaplace(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 A003024.

Row sums are A053763.

The unlabeled version is A361582.

Cf. A189898 (weak components), A361269 (loops allowed), A361591.

Sequence in context: A009759 A127187 A057398 * A373713 A013579 A151814

Adjacent sequences: A361452 A361453 A361454 * A361456 A361457 A361458

Keyword

nonn,tabl

Author

Andrew Howroyd, Mar 16 2023

Status

approved