A005014 Certain subgraphs of a directed graph (inverse binomial transform of A005321).

1, 1, 7, 97, 2911, 180481, 22740607, 5776114177, 2945818230271, 3010626231336961, 6159741269315422207, 25217980756577338515457, 206535262396368402441592831, 3383460668577307168798173757441

Offset: 1

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 = 1..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

Crossrefs

Pairwise sums of A005327.

Programs

Maple

p:=proc(n) if n=0 then 1 else product(2^i-1,i=1..n) fi end: a:=n->(-1)^n+(p(n)+p(n-1))*sum((-1)^j/p(j),j=0..n-1): seq(a(n),n=1..14); # Emeric Deutsch, Jan 23 2005

Mathematica

a[1] = 1; a[n_] := a[n] = (2^n-2)*a[n-1]-(-1)^n; Table[a[n], {n, 1, 14}] (* Jean-François Alcover, Jan 17 2014, after Vladeta Jovovic *)

Formula

a(n) = (-1)^n + (p(n) + p(n-1))Sum_{j=0..n-1} (-1)^j/p(j), where p(0)=1, p(k) = Product_{i=1..k} (2^i - 1) for k > 0. - Emeric Deutsch, Jan 23 2005

a(n) = (2^n-2)*a(n-1) - (-1)^n. - Vladeta Jovovic, Aug 20 2006

G.f.: Sum_{n>=0} (x^n*Product_{i=1..n} (2^i - 1)/(1 + 2^i*x)). - Vladeta Jovovic, Mar 10 2008

Extensions

More terms from Vladeta Jovovic, Aug 20 2006