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

1,2

Links

Table of n, a(n) for n=1..25.

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.

Prog

(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}

Crossrefs

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

Sequence in context: A220726 A347302 A127540 * A319852 A060900 A305850

Adjacent sequences: A339038 A339039 A339040 * A339042 A339043 A339044

Keyword

nonn

Author

Andrew Howroyd, Nov 20 2020

Status

approved