A350914 Triangle read by rows: T(n,k) is the number of unlabeled weakly connected oriented graphs with n arcs and k vertices, k = 1..n+1.

1, 0, 1, 0, 0, 3, 0, 0, 2, 8, 0, 0, 0, 12, 27, 0, 0, 0, 10, 68, 91, 0, 0, 0, 4, 127, 395, 350, 0, 0, 0, 0, 144, 1144, 2170, 1376, 0, 0, 0, 0, 107, 2393, 9139, 11934, 5743, 0, 0, 0, 0, 50, 3767, 28606, 67104, 64892, 24635, 0, 0, 0, 0, 12, 4500, 71583, 288331, 468702, 352286, 108968

Offset

0,6

Links

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

Example

Triangle begins:
  1;
  0, 1;
  0, 0, 3;
  0, 0, 2,  8;
  0, 0, 0, 12,  27;
  0, 0, 0, 10,  68,   91;
  0, 0, 0,  4, 127,  395,  350;
  0, 0, 0,  0, 144, 1144, 2170, 1376;
  ...

Prog

(PARI) \\ See A350734 for G, InvEulerMTS.
T(n)={my(p=InvEulerMTS(sum(i=0, n, G(i, y+O(y^n))*x^i, O(x*x^n)))); vector(n, n, Vec(O(x^n)+polcoef(p, n-1, y)/x, -n))}
{ my(A=T(10)); for(n=1, #A, print(A[n])) }

Crossrefs

Row sums are A350915.

Column sums are A086345.

Cf. A350734 (transpose), A350789 (digraphs).

Sequence in context: A117138 A292255 A362313 * A346607 A095104 A021337

Adjacent sequences: A350911 A350912 A350913 * A350915 A350916 A350917

Keyword

nonn,tabl

Author

Andrew Howroyd, Jan 29 2022

Status

approved