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A101388 Number of n-vertex unlabeled digraphs without endpoints.

%I A101388 #6 Jan 22 2021 16:06:21
%S A101388 1,1,1,8,137,7704,1413982,855543836,1775124241697,12985137979651848,
%T A101388 340909258684048264585,32512676857544231506934756,
%U A101388 11365672344040389664750137465767,14668676509227095069116619104786898732,70315084528883620836175544247562749711989951
%N A101388 Number of n-vertex unlabeled digraphs without endpoints.
%H A101388 Andrew Howroyd, <a href="/A101388/b101388.txt">Table of n, a(n) for n = 0..50</a>
%o A101388 (PARI)
%o A101388 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}
%o A101388 edges(v) = {sum(i=2, #v, sum(j=1, i-1, 2*gcd(v[i],v[j]))) + sum(i=1, #v, v[i]-1)}
%o A101388 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
%Y A101388 Cf. A100548 (labeled case), A004110, A004108, A059166, A059167, A101389.
%K A101388 nonn
%O A101388 0,4
%A A101388 Goran Kilibarda, Zoran Maksimovic, _Vladeta Jovovic_, Jan 14 2005
%E A101388 a(0)=1 prepended and terms a(7) and beyond from _Andrew Howroyd_, Jan 22 2021