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A350734
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Triangle read by rows: T(n,k) is the number of weakly connected oriented graphs on n unlabeled nodes with k arcs, n >= 1, k = 0..n*(n-1)/2.
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6
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1, 0, 1, 0, 0, 3, 2, 0, 0, 0, 8, 12, 10, 4, 0, 0, 0, 0, 27, 68, 127, 144, 107, 50, 12, 0, 0, 0, 0, 0, 91, 395, 1144, 2393, 3767, 4500, 4112, 2740, 1274, 376, 56, 0, 0, 0, 0, 0, 0, 350, 2170, 9139, 28606, 71583, 145600, 244589, 339090, 387458, 361394, 271177, 159872, 71320, 22690, 4604, 456
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OFFSET
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1,6
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LINKS
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EXAMPLE
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Triangle begins:
[1] 1;
[2] 0, 1;
[3] 0, 0, 3, 2;
[4] 0, 0, 0, 8, 12, 10, 4;
[5] 0, 0, 0, 0, 27, 68, 127, 144, 107, 50, 12;
...
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PROG
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(PARI)
InvEulerMTS(p)={my(n=serprec(p, x)-1, q=log(p), vars=variables(p)); sum(i=1, n, moebius(i)*substvec(q + O(x*x^(n\i)), vars, apply(v->v^i, vars))/i)}
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}
edges(v, t) = {prod(i=2, #v, prod(j=1, i-1, my(g=gcd(v[i], v[j])); t(v[i]*v[j]/g)^g )) * prod(i=1, #v, my(c=v[i]); t(c)^((c-1)\2))}
G(n, x)={my(s=0); forpart(p=n, s+=permcount(p)*edges(p, i->1+2*x^i)); s/n!}
row(n)={Vecrev(polcoef(InvEulerMTS(sum(i=0, n, G(i, y)*x^i, O(x*x^n))), n))}
{ for(n=1, 6, print(row(n))) }
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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