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

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

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

Programs

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 *)

Formula

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

Extensions

More terms from Max Alekseyev, May 04 2010

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