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A350749
Triangle read by rows: T(n,k) is the number of oriented graphs on n labeled nodes with k arcs, n >= 0, k = 0..n*(n-1)/2.
1
1, 1, 1, 2, 1, 6, 12, 8, 1, 12, 60, 160, 240, 192, 64, 1, 20, 180, 960, 3360, 8064, 13440, 15360, 11520, 5120, 1024, 1, 30, 420, 3640, 21840, 96096, 320320, 823680, 1647360, 2562560, 3075072, 2795520, 1863680, 860160, 245760, 32768
OFFSET
0,4
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1350 (rows 0..20)
FORMULA
T(n,k) = 2^k * binomial(n*(n-1)/2, k) = A013609(n*(n-1)/2, k).
T(n,k) = [y^k] (1+2*y)^(n*(n-1)/2).
EXAMPLE
Triangle begins:
[0] 1;
[1] 1;
[2] 1, 2;
[3] 1, 6, 12, 8;
[4] 1, 12, 60, 160, 240, 192, 64;
[5] 1, 20, 180, 960, 3360, 8064, 13440, 15360, 11520, 5120, 1024;
...
PROG
(PARI) T(n, k) = 2^k * binomial(n*(n-1)/2, k)
(PARI)
row(n) = {Vecrev((1+2*y)^(n*(n-1)/2))}
{ for(n=0, 6, print(row(n))) }
CROSSREFS
Row sums are A047656.
The unlabeled version is A350733.
Cf. A013609, A350732 (weakly connected), A350731 (strongly connected).
Sequence in context: A325635 A375753 A081064 * A347594 A128534 A002562
KEYWORD
nonn,tabf
AUTHOR
Andrew Howroyd, Feb 15 2022
STATUS
approved