cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A361586 Number of digraphs on n unlabeled nodes in which every node belongs to a directed cycle.

Original entry on oeis.org

1, 0, 1, 5, 90, 5289, 1071691, 712342075, 1585944117738, 12152982231404393, 328276896613548366675, 31834464336872565979301363, 11234630426387288679040317490771, 14576388456695908232721134339830232699, 70075904005979773819582865772534172929477101
Offset: 0

Views

Author

Andrew Howroyd, Mar 16 2023

Keywords

Crossrefs

Column k=0 of A361590.
The labeled version is A086366.
Cf. A350794.

Programs

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.

Original entry on oeis.org

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

Views

Author

Geoffrey Critzer, Mar 16 2023

Keywords

Examples

			Triangle begins:
       1;
       0,      1;
       1,      0,      3;
      18,     21,      0,    25;
    1699,   1080,    774,     0, 543;
  587940, 267665, 103860, 59830,   0, 29281;
  ...
		

Crossrefs

Cf. A086366 (column k=0), A003024 (main diagonal), A053763 (row sums), A361590 (unlabeled version).

Programs

  • 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
Showing 1-2 of 2 results.