A339044 Number of unlabeled connected simple graphs with n edges rooted at one oriented edge.

1, 2, 6, 18, 57, 188, 651, 2336, 8719, 33741, 135185, 559908, 2394326, 10557283, 47943126, 223987316, 1075455181, 5301593544, 26807904317, 138924912857, 737220195148, 4002876571636, 22221898966507, 126042573704637, 729944250603862, 4313430995825272

Offset: 1

Author

Andrew Howroyd, Nov 21 2020

Keywords

• nonn

Crossrefs

Cf. A000664, A002905, A303832, A304072, A339037, A339039, A339040, A339041, A339063.

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, [])/(1+x))}

Formula

G.f.: x*f(x)/((1+x)*g(x)) where f(x) is the g.f. of A339063 and g(x) is the g.f. of A000664.