A307049 Irregular table read by rows: The number of acyclic digraphs on n labeled nodes with k descents.

1, 2, 1, 8, 11, 5, 1, 64, 161, 167, 102, 39, 9, 1, 1024, 3927, 6698, 7185, 5477, 3107, 1329, 423, 96, 14, 1, 32768, 172665, 419364, 656733, 757939, 686425, 504084, 305207, 153333, 63789, 21752, 5959, 1267, 197, 20, 1, 2097152, 14208231, 45263175, 94040848, 145990526, 181444276, 187742937, 165596535

Offset

1,2

References

Archer, K., Gessel, I. M., Graves, C., & Liang, X. (2020). Counting acyclic and strong digraphs by descents. Discrete Mathematics, 343(11), 112041. See Table 3

Links

Table of n, a(n) for n=1..49.

Kassie Archer, Ira M. Gessel, Christina Graves, and Xuming Liang, Counting acyclic and strong digraphs by descents, arXiv:1909.01550 [math.CO], 20 Mar 2020. See Table 3.

K. Archer, C. Graves, Enumerating acyclic digraphs by descents, arXiv:1709.00601 [math.CO], 2017.

Example

     1;
     2    1;
     8   11    5    1;
    64  161  167  102   39    9    1;
  1024 3927 6698 7185 5477 3107 1329 423 96 14 1;
...

Crossrefs

Cf. A003024 (row sums), A006125, A057273, A339590, A339807.

Sequence in context: A192424 A211192 A160614 * A164662 A007026 A160485

Adjacent sequences: A307046 A307047 A307048 * A307050 A307051 A307052

Keyword

nonn,tabf

Author

R. J. Mathar, Mar 21 2019

Status

approved