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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 (list; graph; refs; listen; history; text; internal format)
 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 EXTENSIONS More terms from Vladeta Jovovic, Aug 20 2006 STATUS approved

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Last modified May 9 05:11 EDT 2021. Contains 343688 sequences. (Running on oeis4.)