A350732 - OEIS

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A350732

Triangle read by rows: T(n,k) is the number of weakly connected oriented graphs on n labeled nodes with k arcs, n >= 0, k=0..n*(n-1)/2.

1, 0, 2, 0, 0, 12, 8, 0, 0, 0, 128, 240, 192, 64, 0, 0, 0, 0, 2000, 7104, 13120, 15360, 11520, 5120, 1024, 0, 0, 0, 0, 0, 41472, 234240, 729600, 1578240, 2531840, 3068928, 2795520, 1863680, 860160, 245760, 32768

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1350 (rows 1..20)

EXAMPLE

Triangle begins:

[1] 1;

[2] 0, 2;

[3] 0, 0, 12, 8;

[4] 0, 0, 0, 128, 240, 192, 64;

[5] 0, 0, 0, 0, 2000, 7104, 13120, 15360, 11520, 5120, 1024;

...

PROG

(PARI)

row(n)={Vecrev(n!*polcoef(1 + log(sum(k=0, n, (1+2*y)^(k*(k-1)/2)*x^k/k!, O(x*x^n))), n))}

{ for(n=1, 5, print(row(n))) }

CROSSREFS

Row sums are A054941.

The leading diagonal is A097629.

The unlabeled version is A350734.

Cf. A062735 (digraphs), A350731 (strongly connected).

Sequence in context: A302751 A350909 A244139 * A231031 A061848 A193294

Adjacent sequences: A350729 A350730 A350731 * A350733 A350734 A350735

KEYWORD

nonn,tabf

AUTHOR

Andrew Howroyd, Jan 11 2022

STATUS

approved