A329228
Triangle read by rows: T(n,k) is the number of digraphs on n unlabeled vertices such that every vertex has outdegree k, n >= 1, 0 <= k < n.
Original entry on oeis.org
1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 13, 79, 13, 1, 1, 40, 1499, 1499, 40, 1, 1, 100, 35317, 257290, 35317, 100, 1, 1, 291, 967255, 56150820, 56150820, 967255, 291, 1, 1, 797, 29949217, 14971125930, 111359017198, 14971125930, 29949217, 797, 1
Offset: 1
Triangle begins:
1;
1, 1;
1, 2, 1;
1, 6, 6, 1;
1, 13, 79, 13, 1;
1, 40, 1499, 1499, 40, 1;
1, 100, 35317, 257290, 35317, 100, 1;
1, 291, 967255, 56150820, 56150820, 967255, 291, 1;
...
-
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}
Row(n)={my(s=0); forpart(p=n, s+=permcount(p)*E(p, x+O(x^n))); Vec(s/n!)}
{ for(n=1, 8, print(Row(n))) }
A129524
Number of unlabeled digraphs on n vertices such that every vertex has outdegree 2.
Original entry on oeis.org
0, 0, 1, 6, 79, 1499, 35317, 967255, 29949217, 1033242585, 39323062014, 1637375262965, 74075329383599, 3619112881630497, 189953824713590782, 10661151595417930874, 637230479685691806302, 40415532825383300892418, 2711124591869919503655096
Offset: 1
A185193
Number of unlabeled digraphs on n vertices such that every vertex has outdegree 3.
Original entry on oeis.org
0, 0, 0, 1, 13, 1499, 257290, 56150820, 14971125930, 4829990898461, 1864386642498918, 851204815909786099, 454661054439318678263, 281270600132956104641972, 199701092658236514672384967, 161392692052798327047616107614, 147373164027242947672475065773269
Offset: 1
A185303
Number of unlabeled digraphs on n vertices such that every vertex has outdegree 5.
Original entry on oeis.org
0, 0, 0, 0, 0, 1, 100, 967255, 14971125930, 278086517599356, 6521004095675547914, 197419530111112377546537, 7747427934648623352166753715, 392370903258277676503800999871543, 25436929780226775791085690703723141426, 2090584629532654146005764252197925046719651
Offset: 1
Showing 1-4 of 4 results.