A329228 - OEIS

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

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OFFSET

1,5

LINKS

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

EXAMPLE

Triangle begins:

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;

...

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}

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))) }

CROSSREFS

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

Row sums are A329234.

Sequence in context: A145903 A223257 A173881 * A172373 A174411 A322620

Adjacent sequences: A329225 A329226 A329227 * A329229 A329230 A329231

KEYWORD

nonn,tabl

AUTHOR

Andrew Howroyd, Nov 08 2019

STATUS

approved