A350733 Triangle read by rows: T(n,k) is the number of oriented graphs on n unlabeled nodes with k arcs, n >= 0, k = 0..n*(n-1)/2.

1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 4, 10, 12, 10, 4, 1, 1, 4, 13, 41, 78, 131, 144, 107, 50, 12, 1, 1, 4, 14, 55, 187, 539, 1292, 2500, 3817, 4512, 4112, 2740, 1274, 376, 56, 1, 1, 4, 14, 58, 240, 1009, 3643, 11815, 32538, 76145, 149724, 247329, 340364, 387834, 361450, 271177, 159872, 71320, 22690, 4604, 456

Offset: 0

Author

Andrew Howroyd, Jan 13 2022

Keywords

• nonn
• tabf

Examples

			Triangle begins:
  [0] 1;
  [1] 1;
  [2] 1, 1;
  [3] 1, 1, 3,  2;
  [4] 1, 1, 4, 10, 12, 10,   4;
  [5] 1, 1, 4, 13, 41, 78, 131, 144, 107, 50, 12;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1350 (rows 0..20)

Crossrefs

Row sums are A001174.

Cf. A350734.

Programs

PARI

permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}
edges(v, t) = {prod(i=2, #v, prod(j=1, i-1, my(g=gcd(v[i], v[j])); t(v[i]*v[j]/g)^g )) * prod(i=1, #v, my(c=v[i]); t(c)^((c-1)\2))}
row(n)={my(s=0); forpart(p=n, s+=permcount(p)*edges(p, i->1+2*x^i)); Vecrev(s/n!)}
{ for(n=0, 6, print(row(n))) }