A380252 Triangular array read by rows: T(n,k) is the number of labeled acyclic digraphs on n vertices with exactly k weakly connected components, n>=0, 0<=k<=n.
1, 0, 1, 0, 2, 1, 0, 18, 6, 1, 0, 446, 84, 12, 1, 0, 26430, 2590, 240, 20, 1, 0, 3596762, 175200, 8970, 540, 30, 1, 0, 1111506858, 26568374, 678930, 24010, 1050, 42, 1, 0, 774460794326, 9127077036, 112393736, 2007600, 54740, 1848, 56, 1, 0, 1206342801843750, 7057099207134, 42191272116, 357391608, 5013540, 111636, 3024, 72, 1
Offset: 0
Examples
Triangle T(n,k) begins: 1; 0, 1; 0, 2, 1; 0, 18, 6, 1; 0, 446, 84, 12, 1; 0, 26430, 2590, 240, 20, 1; 0, 3596762, 175200, 8970, 540, 30, 1; ...
Programs
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Mathematica
nn = 8; B[n_] := n! 2^Binomial[n, 2];e[x_] := Sum[x^n/B[n], {n, 0, nn}];egf[ggf_] := Normal[Series[ggf, {x, 0, nn}]] /.Table[x^i -> x^i*2^Binomial[i, 2], {i, 0, nn}]; Table[Drop[(Table[n!, {n, 0, nn}] CoefficientList[Series[Exp[y (Log[egf[1/e[-x]]])], {x, 0, nn}], {x,y}])[[i]], {i + 1, nn + 1}], {i, 1, nn + 1}] // Grid
Formula
E.g.f.: exp(y*log(B(x))) where B(x) = Sum_{n>=0} A003024(n)*x^n/n!.