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A005014
Certain subgraphs of a directed graph (inverse binomial transform of A005321).
(Formerly M4454)
4
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
KEYWORD
nonn
EXTENSIONS
More terms from Vladeta Jovovic, Aug 20 2006
STATUS
approved