A339045 Number of connected loopless multigraphs with n edges rooted at two noninterchangeable vertices whose removal leaves a connected graph.

1, 1, 4, 16, 69, 307, 1433, 6903, 34337, 175457, 919525, 4931233, 27023894, 151142376, 861880778, 5006906170, 29611120248, 178175786593, 1090266839041, 6781364484106, 42858210422338, 275127506187149, 1793418517202096, 11867326044069470, 79695273536227647

Offset

1,3

Links

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

Formula

1/(Product_{k>=1} (1 - x^k)^a(k)) = f(x)/g(x)^2 where x*f(x) is the g.f. of A339037 and g(x) is the g.f. of A339036.

Prog

(PARI) \\ See A339065 for G.
InvEulerT(v)={my(p=log(1+x*Ser(v))); dirdiv(vector(#v, n, polcoef(p, n)), vector(#v, n, 1/n))}
seq(n)={my(A=O(x*x^n), g=G(2*n, x+A, []), gr=G(2*n, x+A, [1])/g); InvEulerT(Vec(-1+G(2*n, x+A, [1, 1])/(g*gr^2)))}

Crossrefs

Cf. A338999, A339036, A339037, A339065.

Sequence in context: A354121 A297203 A231297 * A341255 A231358 A000303

Adjacent sequences: A339042 A339043 A339044 * A339046 A339047 A339048

Keyword

nonn

Author

Andrew Howroyd, Nov 25 2020

Status

approved