OFFSET
0,4
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.
PROG
(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))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 24 2020
STATUS
approved