A327372 Triangle read by rows where T(n,k) is the number of unlabeled simple graphs covering n vertices with exactly k endpoints (vertices of degree 1).

1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 3, 1, 1, 1, 1, 11, 5, 4, 1, 2, 0, 62, 29, 18, 6, 4, 2, 1, 510, 225, 101, 32, 13, 4, 3, 0, 7459, 2674, 842, 223, 72, 19, 9, 3, 1, 197867, 50834, 10784, 2171, 504, 115, 34, 9, 4, 0, 9808968, 1653859, 228863, 32322, 5268, 944, 209, 46, 16, 4, 1

Offset: 0

Author

Gus Wiseman, Sep 04 2019

Keywords

• nonn
• tabl

Examples

			Triangle begins:
   1
   0  0
   0  0  1
   1  0  1  0
   3  1  1  1  1
  11  5  4  1  2  0
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)
• Gus Wiseman, The unlabeled graphs covering 5 vertices with k endpoints.

Crossrefs

Row sums are A002494.

Column k = 0 is A261919.

The non-covering version is A327371.

The labeled version is A327377.

Cf. A000088, A004110, A294217, A327227, A327369, A327370.

Programs

PARI

\\ Needs G(n) defined in A327371.
T(n)={my(v=Vec(G(n)*(1 - x))); vector(#v, n, Vecrev(v[n], n))}
my(A=T(10)); for(n=1, #A, print(A[n])) \\ Andrew Howroyd, Jan 11 2024

Formula

Column-wise first differences of A327371.

Extensions

Terms a(21) and beyond from Andrew Howroyd, Sep 11 2019