OFFSET
0,9
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325
EXAMPLE
Triangle begins:
1
1 1
0 1 1
0 1 3 2
0 0 3 6 3
0 0 2 11 14 6
0 0 1 13 35 33 11
Non-isomorphic representatives of the graphs counted in row 4:
{{2}{3}{12}{13}} {{4}{12}{23}{34}} {{13}{24}{35}{45}}
{{2}{3}{13}{23}} {{4}{13}{23}{34}} {{14}{25}{35}{45}}
{{3}{12}{13}{23}} {{4}{13}{24}{34}} {{15}{25}{35}{45}}
{{4}{14}{24}{34}}
{{12}{13}{24}{34}}
{{14}{23}{24}{34}}
PROG
(PARI)
InvEulerMT(u)={my(n=#u, p=log(1+x*Ser(u)), vars=variables(p)); Vec(serchop( sum(i=1, n, moebius(i)*substvec(p + O(x*x^(n\i)), vars, apply(v->v^i, vars))/i), 1))}
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)^g )) * prod(i=1, #v, my(c=v[i]); t(c)^((c+1)\2)*if(c%2, 1, t(c/2)))}
G(n, x)={my(s=0); forpart(p=n, s+=permcount(p)*edges(p, i->1+x^i)); s/n!}
T(n)={Mat([Col(p+O(y^n), -n) | p<-InvEulerMT(vector(n, k, G(k, y + O(y^n))))])}
{my(A=T(10)); for(n=1, #A, print(A[n, 1..n]))} \\ Andrew Howroyd, Oct 22 2019
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Nov 26 2018
EXTENSIONS
Terms a(28) and beyond from Andrew Howroyd, Oct 22 2019
STATUS
approved