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.

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

Author

Andrew Howroyd, Nov 08 2019

Keywords

• nonn
• tabl

Examples

			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;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1275

Crossrefs

Columns k=0..5 are A000012, A001373, A129524, A185193, A185194, A185303.

Row sums are A329234.

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}
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))) }