A329228 - OEIS

%I #10 Nov 08 2019 15:34:48

%S 1,1,1,1,2,1,1,6,6,1,1,13,79,13,1,1,40,1499,1499,40,1,1,100,35317,

%T 257290,35317,100,1,1,291,967255,56150820,56150820,967255,291,1,1,797,

%U 29949217,14971125930,111359017198,14971125930,29949217,797,1

%N 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.

%H Andrew Howroyd, <a href="/A329228/b329228.txt">Table of n, a(n) for n = 1..1275</a>

%e Triangle begins:

%e   1;

%e   1,   1;

%e   1,   2,      1;

%e   1,   6,      6,        1;

%e   1,  13,     79,       13,        1;

%e   1,  40,   1499,     1499,       40,      1;

%e   1, 100,  35317,   257290,    35317,    100,   1;

%e   1, 291, 967255, 56150820, 56150820, 967255, 291, 1;

%e   ...

%o (PARI)

%o 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}

%o 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}

%o Row(n)={my(s=0); forpart(p=n, s+=permcount(p)*E(p, x+O(x^n))); Vec(s/n!)}

%o { for(n=1, 8, print(Row(n))) }

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

%Y Row sums are A329234.

%K nonn,tabl

%O 1,5

%A _Andrew Howroyd_, Nov 08 2019