A303832 The number of edge-rooted unlabeled connected graphs with n edges.

1, 1, 4, 10, 32, 101, 346, 1220, 4517, 17338, 69107, 285009, 1215015, 5344224, 24223641, 113001129, 541913075, 2668817544, 13484234188, 69831773559, 370361639587, 2009988998148, 11153858854425, 63242354288220, 366140089188603, 2163036956456422, 13031489297543608

Offset: 1

Author

R. J. Mathar, May 04 2018

Keywords

• nonn

Examples

			a(1)=1: the connected graph with 1 edge (which is rooted).
a(2)=1: the connected graph with 2 edges (one rooted).
a(3)=4: the triangle graph with one choice of rooting, the linear tree with either the middle or a terminating edge rooted, the star graph with one edge rooted.
		

Crossrefs

Cf. A126133 (not necessarily connected), A000664, A303830 (by number of nodes).

Cf. A002905, A339039, A339040, A339041, A339044.

Programs

PARI

\\ See A339063 for G.
seq(n)={my(A=O(x*x^n)); Vec((G(2*n, x+A, [1, 1]) + G(2*n, x+A, [2]))/(2*G(2*n, x+A, [])*(1+x)))} \\ Andrew Howroyd, Nov 21 2020

Formula

G.f. A(x) satisfies: A(x)*A000664(x) = A126133(x).