A005014 - OEIS

%I M4454 #32 Apr 14 2021 20:07:17

%S 1,1,7,97,2911,180481,22740607,5776114177,2945818230271,

%T 3010626231336961,6159741269315422207,25217980756577338515457,

%U 206535262396368402441592831,3383460668577307168798173757441

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

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Michael De Vlieger, <a href="/A005014/b005014.txt">Table of n, a(n) for n = 1..81</a>

%H E. Andresen and K. Kjeldsen, <a href="http://dx.doi.org/10.1016/0012-365X(76)90054-6">On certain subgraphs of a complete transitively directed graph</a>, Discrete Math. 14 (1976), no. 2, 103-119.

%H Hsien-Kuei Hwang, Emma Yu Jin, and Michael J. Schlosser, <a href="https://arxiv.org/abs/2012.13570">Asymptotics and statistics on Fishburn Matrices: dimension distribution and a conjecture of Stoimenow</a>, arXiv:2012.13570 [math.CO], 2020.

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F 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

%F a(n) = (2^n-2)*a(n-1) - (-1)^n. - _Vladeta Jovovic_, Aug 20 2006

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

%p 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

%t 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_ *)

%Y Pairwise sums of A005327.

%K nonn

%O 1,3

%A _N. J. A. Sloane_

%E More terms from _Vladeta Jovovic_, Aug 20 2006