OFFSET
0,14
COMMENTS
An endpoint is a vertex that appears in only one edge. Equivalently, the degree of every vertex >= 2.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)
EXAMPLE
Triangle begins:
1;
0, 0;
0, 0, 1;
0, 0, 1, 1;
0, 0, 1, 2, 2;
0, 0, 1, 3, 5, 2;
0, 0, 1, 5, 14, 10, 4;
0, 0, 1, 6, 25, 33, 18, 4;
0, 0, 1, 8, 46, 96, 90, 31, 7;
0, 0, 1, 10, 75, 227, 330, 194, 52, 8;
0, 0, 1, 12, 117, 494, 1033, 962, 416, 82, 12;
...
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, 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) = {my(s=O(x*x^n)); sum(k=0, n, forpart(p=k, s+=permcount(p) / edges(p, w->1-y^w+O(y*y^n)) * x^k * prod(i=1, #p, 1-(y*x)^p[i], 1+O(x^(n-k+1))) / k!)); s*(1-x)}
T(n)={my(r=Vec(substvec(G(n), [x, y], [y, x]))); vector(#r, i, Vecrev(Pol(r[i]), i)) }
{ my(A=T(10)); for(i=1, #A, print(A[i])) }
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Feb 08 2024
STATUS
approved