A101388 Number of n-vertex unlabeled digraphs without endpoints.
1, 1, 1, 8, 137, 7704, 1413982, 855543836, 1775124241697, 12985137979651848, 340909258684048264585, 32512676857544231506934756, 11365672344040389664750137465767, 14668676509227095069116619104786898732, 70315084528883620836175544247562749711989951
Offset: 0
Keywords
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..50
Programs
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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, 2*gcd(v[i],v[j]))) + sum(i=1, #v, v[i]-1)} seq(n)=Vec(sum(k=0, n, my(s=0); forpart(p=k, s+=permcount(p) * 2^edges(p) * prod(i=1, #p, my(d=p[i]); (1-x^d)^3 + O(x*x^(n-k))) ); x^k*s/k!)/(1-x^2)) \\ Andrew Howroyd, Jan 22 2021
Extensions
a(0)=1 prepended and terms a(7) and beyond from Andrew Howroyd, Jan 22 2021