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

0,3

Links

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

Prog

(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!)}

Crossrefs

Row sums of A329228.

Cf. A000273.

Sequence in context: A000609 A245079 A167008 * A238638 A240973 A102449

Adjacent sequences: A329231 A329232 A329233 * A329235 A329236 A329237

Keyword

nonn

Author

Andrew Howroyd, Nov 08 2019

Status

approved