A005331 Certain subgraphs of a directed graph (binomial transform of A005321). (Formerly M1531)

1, 2, 5, 20, 179, 4082, 218225, 25316720, 6135834479, 3047003143022, 3067545380897645, 6223557209578656620, 25360384878802358268779, 207167485813280961035481962, 3389045635023473628621934703465, 110960673463328354866093662279119720, 7268699514166911556909103208203294815079

Offset

0,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Michael De Vlieger, Table of n, a(n) for n = 0..81

E. Andresen and K. Kjeldsen, On certain subgraphs of a complete transitively directed graph, Discrete Math. 14 (1976), no. 2, 103-119.

Hsien-Kuei Hwang, Emma Yu Jin, and Michael J. Schlosser, Asymptotics and statistics on Fishburn Matrices: dimension distribution and a conjecture of Stoimenow, arXiv:2012.13570 [math.CO], 2020.

N. J. A. Sloane, Transforms

Formula

a(n) = Sum_{j=0..n} binomial(n,j)*A005321(j).

Mathematica

Block[{nn = 16, s}, s = CoefficientList[Series[Sum[x^n*Product[(2^i - 1)/(1 + (2^i - 1)*x), {i, n}], {n, 0, #}], {x, 0, #}], x] &@ nn; Array[Sum[Binomial[#, j] s[[j + 1]], {j, 0, #}] &, nn + 1, 0]] (* Michael De Vlieger, Apr 13 2021, after Jean-François Alcover at A005321 *)

Crossrefs

Sequence in context: A181076 A156871 A058109 * A261005 A158872 A308522

Adjacent sequences: A005328 A005329 A005330 * A005332 A005333 A005334

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

More terms from Max Alekseyev, May 04 2010

a(15)-a(16) from Michael De Vlieger, Apr 13 2021

Status

approved