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A361592
Triangular array read by rows. T(n,k) is the number of labeled digraphs on [n] with exactly k strongly connected components of size 1, n>=0, 0<=k<=n.
3
1, 0, 1, 1, 0, 3, 18, 21, 0, 25, 1699, 1080, 774, 0, 543, 587940, 267665, 103860, 59830, 0, 29281, 750744901, 225144360, 64169325, 19791000, 10110735, 0, 3781503, 3556390155318, 672637205149, 126726655860, 29445913175, 7939815030, 3767987307, 0, 1138779265
OFFSET
0,6
LINKS
E. de Panafieu and S. Dovgal, Symbolic method and directed graph enumeration, arXiv:1903.09454 [math.CO], 2019.
R. W. Robinson, Counting digraphs with restrictions on the strong components, Combinatorics and Graph Theory '95 (T.-H. Ku, ed.), World Scientific, Singapore (1995), 343-354.
EXAMPLE
Triangle begins:
1;
0, 1;
1, 0, 3;
18, 21, 0, 25;
1699, 1080, 774, 0, 543;
587940, 267665, 103860, 59830, 0, 29281;
...
MATHEMATICA
nn = 7; B[n_] := n! 2^Binomial[n, 2]; strong = Select[Import["https://oeis.org/A003030/b003030.txt", "Table"], Length@# == 2 &][[All, 2]]; s[x_] := Total[strong Table[x^i/i!, {i, 1, 58}]]; ggfz[egfx_] := Normal[Series[egfx, {x, 0, nn}]] /.Table[x^i -> z^i/2^Binomial[i, 2], {i, 0, nn}]; Table[Take[(Table[B[n], {n, 0, nn}] CoefficientList[Series[1/ggfz[Exp[-(s[x] - x + u x)]], {z, 0, nn}], {z, u}])[[i]], i], {i, 1, nn + 1}] // Grid
CROSSREFS
Cf. A086366 (column k=0), A003024 (main diagonal), A053763 (row sums), A361590 (unlabeled version).
Sequence in context: A339631 A195998 A291167 * A174029 A103715 A131860
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Mar 16 2023
STATUS
approved