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%I #5 Nov 08 2019 15:35:38
%S 1,1,2,4,14,107,3080,328126,114236734,141361169088,565835083485352,
%T 8280254429732072354,401805920591472162735162,
%U 73001963040583041357650757758,44826822610575086782059677501403310,104876792026574880566541471182849498480154,841219618683014295050378892027503163229521608514
%N Number of digraphs on n unlabled vertices such that every vertex has the same outdegree.
%H Andrew Howroyd, <a href="/A329234/b329234.txt">Table of n, a(n) for n = 0..50</a>
%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 E(v, x) = {my(r=1/(1-x)); for(i=1, #v, r=serconvol(r, prod(j=1, #v, my(g=gcd(v[i], v[j])); (1 + x^(v[j]/g))^g)/(1 + x))); r}
%o a(n)={if(n<1, n==0, my(s=0); forpart(p=n, s+=permcount(p)*E(p, x+O(x^n))); vecsum(Vec(s))/n!)}
%Y Row sums of A329228.
%Y Cf. A000273.
%K nonn
%O 0,3
%A _Andrew Howroyd_, Nov 08 2019