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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.

%I A329228 #10 Nov 08 2019 15:34:48
%S A329228 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 A329228 257290,35317,100,1,1,291,967255,56150820,56150820,967255,291,1,1,797,
%U A329228 29949217,14971125930,111359017198,14971125930,29949217,797,1
%N 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.
%H A329228 Andrew Howroyd, <a href="/A329228/b329228.txt">Table of n, a(n) for n = 1..1275</a>
%e A329228 Triangle begins:
%e A329228   1;
%e A329228   1,   1;
%e A329228   1,   2,      1;
%e A329228   1,   6,      6,        1;
%e A329228   1,  13,     79,       13,        1;
%e A329228   1,  40,   1499,     1499,       40,      1;
%e A329228   1, 100,  35317,   257290,    35317,    100,   1;
%e A329228   1, 291, 967255, 56150820, 56150820, 967255, 291, 1;
%e A329228   ...
%o A329228 (PARI)
%o A329228 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 A329228 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 A329228 Row(n)={my(s=0); forpart(p=n, s+=permcount(p)*E(p, x+O(x^n))); Vec(s/n!)}
%o A329228 { for(n=1, 8, print(Row(n))) }
%Y A329228 Columns k=0..5 are A000012, A001373, A129524, A185193, A185194, A185303.
%Y A329228 Row sums are A329234.
%K A329228 nonn,tabl
%O A329228 1,5
%A A329228 _Andrew Howroyd_, Nov 08 2019