A350749 - OEIS

%I #8 Feb 16 2022 15:33:26

%S 1,1,1,2,1,6,12,8,1,12,60,160,240,192,64,1,20,180,960,3360,8064,13440,

%T 15360,11520,5120,1024,1,30,420,3640,21840,96096,320320,823680,

%U 1647360,2562560,3075072,2795520,1863680,860160,245760,32768

%N 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.

%H Andrew Howroyd, <a href="/A350749/b350749.txt">Table of n, a(n) for n = 0..1350</a> (rows 0..20)

%F T(n,k) = 2^k * binomial(n*(n-1)/2, k) = A013609(n*(n-1)/2, k).

%F T(n,k) = [y^k] (1+2*y)^(n*(n-1)/2).

%e Triangle begins:

%e   [0] 1;

%e   [1] 1;

%e   [2] 1,  2;

%e   [3] 1,  6,  12,   8;

%e   [4] 1, 12,  60, 160,  240,  192,    64;

%e   [5] 1, 20, 180, 960, 3360, 8064, 13440, 15360, 11520, 5120, 1024;

%e   ...

%o (PARI) T(n,k) = 2^k * binomial(n*(n-1)/2, k)

%o (PARI)

%o row(n) = {Vecrev((1+2*y)^(n*(n-1)/2))}

%o { for(n=0, 6, print(row(n))) }

%Y Row sums are A047656.

%Y The unlabeled version is A350733.

%Y Cf. A013609, A350732 (weakly connected), A350731 (strongly connected).

%K nonn,tabf

%O 0,4

%A _Andrew Howroyd_, Feb 15 2022