A331584 Number of series-reduced connected labeled graphs with n edges.

1, 1, 0, 4, 5, 96, 548, 7908, 84696, 1331840, 20255774, 372819387, 7170089146, 154824436840, 3558826861734, 88938133663711, 2367074592366594, 67402755251544804, 2034875403034891874, 65102692993820702700, 2196725886835707259041, 78036983096041464230268

Offset: 0

Author

Andrew Howroyd, Jan 24 2020

Keywords

• nonn

Comments

Series-reduced graphs are also called homeomorphically irreducible graphs and are the graphs without vertices of degree 2.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..100
• D. M. Jackson and J. W. Reilly, The enumeration of homeomorphically irreducible labeled graphs, J. Combin. Theory, B 19 (1975), 272-286.

Crossrefs

Row sums of A331437.

Column sums of A331438.

Cf. A003515.

Programs

PARI

\\ See Jackson & Reilly link for e.g.f.
H(n,y) = {my(A=O(x*x^n)); (exp(y*x/2 - (y*x)^2/4 + A)/sqrt(1 + y*x + A))*sum(k=0, n, ((1 + y)*exp(-y^2*x/(1+y*x) + A))^binomial(k,2) * (x*exp((y^3*x^2 + A)/(2*(1 + y*x))))^k / k!)}
seq(n)={Vec(subst(Pol(serlaplace(log(H(n, y+O(y^n))))), x, 1))}