OFFSET
2,4
REFERENCES
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 2..2661 (rows 2..20)
R. J. Mathar, Statistics on Small Graphs, arXiv:1709.09000 (2017) Table 75.
EXAMPLE
1,1;
0,3,4,4,1,1;
0,0,8,22,37,47,38,27,13,5,1,1;
the last batch giving the numbers of connected digraphs with 4 nodes and from 1 to 12 arcs.
PROG
(PARI)
InvEulerMTS(p)={my(n=serprec(p, x)-1, q=log(p), vars=variables(p)); sum(i=1, n, moebius(i)*substvec(q + O(x*x^(n\i)), vars, apply(v->v^i, vars))/i)}
permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}
edges(v, t) = {prod(i=2, #v, prod(j=1, i-1, my(g=gcd(v[i], v[j])); t(v[i]*v[j]/g)^(2*g) )) * prod(i=1, #v, my(c=v[i]); t(c)^(c-1))}
G(n, x)={my(s=0); forpart(p=n, s+=permcount(p)*edges(p, i->1+x^i)); s/n!}
row(n)={Vecrev(polcoef(InvEulerMTS(sum(i=0, n, G(i, y)*x^i, O(x*x^n))), n)/y)}
{ for(n=2, 6, print(row(n))) } \\ Andrew Howroyd, Jan 28 2022
CROSSREFS
KEYWORD
easy,nonn,tabf
AUTHOR
Vladeta Jovovic, Apr 21 2000
STATUS
approved