login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A101388
Number of n-vertex unlabeled digraphs without endpoints.
3
1, 1, 1, 8, 137, 7704, 1413982, 855543836, 1775124241697, 12985137979651848, 340909258684048264585, 32512676857544231506934756, 11365672344040389664750137465767, 14668676509227095069116619104786898732, 70315084528883620836175544247562749711989951
OFFSET
0,4
LINKS
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, 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
CROSSREFS
Cf. A100548 (labeled case), A004110, A004108, A059166, A059167, A101389.
Sequence in context: A134053 A136472 A145404 * A281684 A050789 A274669
KEYWORD
nonn
AUTHOR
Goran Kilibarda, Zoran Maksimovic, Vladeta Jovovic, Jan 14 2005
EXTENSIONS
a(0)=1 prepended and terms a(7) and beyond from Andrew Howroyd, Jan 22 2021
STATUS
approved