OFFSET
0,9
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1274 (terms 0..119 from R. J. Mathar)
R. J. Mathar, Statistics on Small Graphs, arXiv:1709.09000 [math.CO], 2017; see Section 4.
Brendan McKay and Adolfo Piperno, nauty and Traces. [nauty and Traces are programs for computing automorphism groups of graphs and digraphs.]
B. D. McKay and A. Piperno, Practical Graph Isomorphism, II, J. Symbolic Computation 60 (2013), 94-112.
Gordon Royle, Small Multigraphs.
FORMULA
EXAMPLE
Triangle T(n,k) (with rows n >= 0 and columns k >= 1) begins as follows:
1;
0, 1;
0, 1, 1;
0, 1, 2, 2;
0, 1, 3, 5, 3;
0, 1, 4, 11, 11, 6;
0, 1, 6, 22, 34, 29, 11;
...
PROG
(PARI)
EulerT(v)={my(p=exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1); Vec(p/x, -#v)}
InvEulerMT(u)={my(n=#u, p=log(1+x*Ser(u)), vars=variables(p)); Vec(sum(i=1, n, moebius(i)*substvec(p + 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, x)={sum(i=2, #v, sum(j=1, i-1, my(g=gcd(v[i], v[j])); g*x^(v[i]*v[j]/g))) + sum(i=1, #v, my(t=v[i]); ((t-1)\2)*x^t + if(t%2, 0, x^(t/2)))}
G(n, m)={my(s=0); forpart(p=n, s+=permcount(p)*EulerT(Vec(edges(p, x) + O(x*x^m), -m))); s/n!}
R(n)={Mat(apply(p->Col(p+O(y^n), -n), InvEulerMT(vector(n, k, 1 + y*Ser(G(k, n-1), y)))))}
{ my(A=R(10)); for(n=1, #A, for(k=1, n, print1(A[n, k], ", ")); print) } \\ Andrew Howroyd, May 14 2018
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alberto Tacchella, Jul 04 2011
STATUS
editing