A005014 Certain subgraphs of a directed graph (inverse binomial transform of A005321). (Formerly M4454)

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

Offset

1,3

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

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

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 *)

Crossrefs

Pairwise sums of A005327.

Sequence in context: A027837 A174315 A046908 * A201063 A333246 A335922

Adjacent sequences: A005011 A005012 A005013 * A005015 A005016 A005017

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, Aug 20 2006

Status

approved