A339041 Number of unlabeled connected simple graphs with n edges rooted at two indistinguishable vertices.

1, 2, 7, 21, 73, 255, 946, 3618, 14376, 58957, 249555, 1087828, 4878939, 22488282, 106432530, 516783762, 2572324160, 13116137104, 68461594211, 365559412868, 1995532789212, 11129600885183, 63381069498524, 368338847181336, 2183239817036378

Offset: 1

Author

Andrew Howroyd, Nov 20 2020

Keywords

• nonn

Crossrefs

Cf. A000664, A002905, A303831, A303832, A339039, A339040, A339043, A339044, A339063, A339064.

Programs

PARI

\\ See A339063 for G.
seq(n)={my(A=O(x*x^n), g=G(2*n, x+A, []), gr=G(2*n, x+A, [1])/g); Vec(G(2*n, x+A, [1, 1])/g - gr^2 + G(2*n, x+A, [2])/g - subst(gr, x, x^2))/2}

Formula

G.f.: f(x)/g(x) - (r(x)^2 + r(x^2))/2 where f(x), g(x) and r(x) are the g.f.'s of A339064, A000664 and A339039.