A329234 Number of digraphs on n unlabled vertices such that every vertex has the same outdegree.

1, 1, 2, 4, 14, 107, 3080, 328126, 114236734, 141361169088, 565835083485352, 8280254429732072354, 401805920591472162735162, 73001963040583041357650757758, 44826822610575086782059677501403310, 104876792026574880566541471182849498480154, 841219618683014295050378892027503163229521608514

Offset: 0

Author

Andrew Howroyd, Nov 08 2019

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50

Crossrefs

Row sums of A329228.

Cf. A000273.

Programs

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}
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}
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!)}