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A350731
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Triangle read by rows: T(n,k) is the number of strongly connected oriented graphs on n labeled nodes with k arcs, n >= 1, k=0..n*(n-1)/2.
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5
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1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 6, 36, 24, 0, 0, 0, 0, 0, 24, 480, 1940, 2970, 2040, 544, 0, 0, 0, 0, 0, 0, 120, 5040, 51330, 221910, 527940, 772080, 722250, 426420, 146160, 22320, 0, 0, 0, 0, 0, 0, 0, 720, 52920, 1026060, 8810970, 43268442, 138984510
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OFFSET
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1,7
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LINKS
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EXAMPLE
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Triangle begins:
[1] 1;
[2] 0, 0;
[3] 0, 0, 0, 2;
[4] 0, 0, 0, 0, 6, 36, 24;
[5] 0, 0, 0, 0, 0, 24, 480, 1940, 2970, 2040, 544;
...
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PROG
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(PARI)
OrientedGgf(n, y=1) = {sum(k=0, n, ((1+2*y)/(1+y))^(k*(k-1)/2)*x^k/k!, O(x*x^n) )}
StrongO(n, y=1) = {my(g=serconvol(1/OrientedGgf(n, y), sum(k=0, n, x^k*(1+y)^(k*(k-1)/2), O(x*x^n)))); Vec(serlaplace(-log(g)))}
row(n)={Vecrev(StrongO(n, 'y)[n], n*(n-1)/2+1)}
{ 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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