OFFSET
0,10
COMMENTS
Homeomorphically irreducible graphs are graphs without vertices of degree 2. - Andrew Howroyd, Jan 24 2020
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows n = 0..50)
D. M. Jackson and J. W. Reilly, The enumeration of homeomorphically irreducible labeled graphs, J. Combin. Theory, B 19 (1975), 272-286. See Table III.
EXAMPLE
Triangle begins:
1;
0, 1;
0, 0, 0;
0, 0, 0, 4;
0, 0, 0, 0, 5;
0, 0, 0, 0, 0, 96;
0, 0, 0, 1, 0, 120, 427;
0, 0, 0, 0, 20, 180, 1260, 6448;
0, 0, 0, 0, 15, 420, 3780, 23520, 56961;
...
PROG
(PARI) \\ See Jackson & Reilly 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!)}
T(n) = {Mat([Col(p, -n) | p<-Vec(serlaplace(log(H(n, y + O(y^n)))))])}
{ my(A=T(10)); for(n=1, #A, print(A[n, 1..n])) } \\ Andrew Howroyd, Jan 24 2020
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Jan 19 2020
EXTENSIONS
Terms a(44) and beyond from Andrew Howroyd, Jan 24 2020
STATUS
approved