A126067 - OEIS

%I #11 Apr 20 2020 00:26:53

%S 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 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 463,683,918,1185,1394,1550,1590,1550,1394,1185,918,683,463,295,164,91,42,20,7,3,1,1

%N 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 Andrew Howroyd, <a href="/A126067/b126067.txt">Table of n, a(n) for n = 0..2680</a> (rows 0..20)

%e Triangle begins:

%e   1;

%e   1;

%e   1,1,1;

%e   1,1,2,2,2,1,1;

%e   1,1,3,5,9,10,12,10,9,5,3,1,1;

%e   1,1,3,6,15,24,41,57,77,84,90,84,77,57,41,24,15,6,3,1,1;

%e   ....

%o (PARI)

%o 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 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 Row(n) = {my(s=0); forpart(p=n, s+=permcount(p)*edges(p, i->1+x^i)); Vecrev(s)/n!}

%o { for(n=0, 5, print(Row(n))) } \\ _Andrew Howroyd_, Apr 19 2020

%Y Row sums are A002499.

%Y Cf. A052283, A126066.

%K nonn,tabf

%O 0,8

%A _Vladeta Jovovic_, Feb 28 2007

%E a(0)=1 prepended and terms a(46) and beyond from _Andrew Howroyd_, Apr 19 2020