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A005014 Certain subgraphs of a directed graph (inverse binomial transform of A005321).
(Formerly M4454)
3
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

Table of n, a(n) for n=1..14.

E. Andresen, K. Kjeldsen, On certain subgraphs of a complete transitively directed graph, Discrete Math. 14 (1976), no. 2, 103-119.

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

MATHEMATICA

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

CROSSREFS

Pairwise sums of A005327.

Sequence in context: A027837 A174315 A046908 * A201063 A157035 A022008

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

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Last modified October 24 06:43 EDT 2017. Contains 293836 sequences.