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A126067 Triangle read by rows: T(n,k) is the number of unlabeled self-converse digraphs with n nodes and k arcs, k=0..n*(n-1).

%I A126067 #11 Apr 20 2020 00:26:53
%S A126067 1,1,1,1,1,1,1,2,2,2,1,1,1,1,3,5,9,10,12,10,9,5,3,1,1,1,1,3,6,15,24,
%T A126067 41,57,77,84,90,84,77,57,41,24,15,6,3,1,1,1,1,3,7,20,42,91,164,295,
%U A126067 463,683,918,1185,1394,1550,1590,1550,1394,1185,918,683,463,295,164,91,42,20,7,3,1,1
%N A126067 Triangle read by rows: T(n,k) is the number of unlabeled self-converse digraphs with n nodes and k arcs, k=0..n*(n-1).
%H A126067 Andrew Howroyd, <a href="/A126067/b126067.txt">Table of n, a(n) for n = 0..2680</a> (rows 0..20)
%e A126067 Triangle begins:
%e A126067   1;
%e A126067   1;
%e A126067   1,1,1;
%e A126067   1,1,2,2,2,1,1;
%e A126067   1,1,3,5,9,10,12,10,9,5,3,1,1;
%e A126067   1,1,3,6,15,24,41,57,77,84,90,84,77,57,41,24,15,6,3,1,1;
%e A126067   ....
%o A126067 (PARI)
%o A126067 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 A126067 edges(v, t) = {prod(i=2, #v, prod(j=1, i-1, my(c=gcd(v[i], v[j])*if(v[i]*v[j]%2==0, 2, 1)); t(2*v[i]*v[j]/c)^c)) * prod(i=1, #v, my(c=v[i]); if(c%2, t(2*c)^(c\2), t(c)^(c-1-c%4/2)*t(c/2)^(c%4)))}
%o A126067 Row(n) = {my(s=0); forpart(p=n, s+=permcount(p)*edges(p, i->1+x^i)); Vecrev(s)/n!}
%o A126067 { for(n=0, 5, print(Row(n))) } \\ _Andrew Howroyd_, Apr 19 2020
%Y A126067 Row sums are A002499.
%Y A126067 Cf. A052283, A126066.
%K A126067 nonn,tabf
%O A126067 0,8
%A A126067 _Vladeta Jovovic_, Feb 28 2007
%E A126067 a(0)=1 prepended and terms a(46) and beyond from _Andrew Howroyd_, Apr 19 2020