OFFSET
1,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..50
FORMULA
EXAMPLE
a(3)=4: one choice to mark two roots in the triangular graph; one choice to mark the two leaves in the linear graph; two choices to mark the center node and a leave (1st root in the center or 2nd root in the center) in the linear graph.
PROG
(PARI)
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) = {sum(i=2, #v, sum(j=1, i-1, gcd(v[i], v[j]))) + sum(i=1, #v, v[i]\2)}
cross(u, v) = {sum(i=1, #u, sum(j=1, #v, gcd(u[i], v[j])))}
S(n, r)={my(t=#r+1); vector(n+1, n, if(n<t, 0, my(s=0); forpart(p=n-t, s+=permcount(p)*(2^(edges(p))*(2^cross(r, p)))); s/(n-t)!))}
seq(n)={my(g=Ser(S(n, []))); Vec(2*Ser(S(n, [1, 1]))/g - (Ser(S(n, [1]))/g)^2, -n)} \\ Andrew Howroyd, Sep 07 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Brendan McKay, May 05 2018
EXTENSIONS
Terms a(13) and beyond from Andrew Howroyd, Sep 07 2019
STATUS
approved