A369290 Number of unlabeled simple graphs without endpoints with n edges.

1, 0, 0, 1, 1, 2, 6, 10, 25, 68, 182, 538, 1748, 5935, 21585, 82904, 334037, 1406934, 6167455, 28033776, 131770437, 638956188, 3189940453, 16369201031, 86214798929, 465480395911, 2573390342437, 14553415319929, 84118459655982, 496514424803358, 2990633679878654

Offset: 0

Author

Andrew Howroyd, Jan 30 2024

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50

Crossrefs

Row sums of A369932.

Cf. A004110 (n vertices), A307316 (multigraph), A342556 (connected).

Programs

PARI

\\ See also A369932 for a more efficient program.
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)))}
seq(n)={my(s=0); forpart(p=2*n, s+=permcount(p)*prod(i=1, #p, 1-x^p[i])*edges(p, w->1+x^w + O(x*x^n))); Vec(s/(2*n)!)}

Formula

Euler transform of A342556.