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A329228
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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.
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9
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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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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,5
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LINKS
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EXAMPLE
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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;
...
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PROG
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(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))) }
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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