OFFSET
1,4
COMMENTS
q-Subfactorial for q=2. - Vladimir Reshetnikov, Sep 12 2016
REFERENCES
T. L. Greenough, Enumeration of interval orders without duplicated holdings, Preprint, circa 1976.
T. L. Greenough and T. Lockman, Representation and enumeration of interval orders and semiorders, Ph.D. Thesis, Dartmouth, 1976.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..50
E. Andresen and K. Kjeldsen, On certain subgraphs of a complete transitively directed graph, Discrete Math. 14 (1976), no. 2, 103-119.
T. L. Greenough, Enumeration of interval orders without duplicated holdings, Preprint, circa 1976. [Annotated scanned copy]
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
For n>1, a(n) = (2^(n-1)-1)*a(n-1) + (-1)^(n-1). - Max Alekseyev, Feb 23 2012
a(n) = p(n-1)*sum((-1)^j/p(j), j=0..n-1), where p(0) = 1, p(k) = product(2^i-1, i=1..k) for k>0. - Emeric Deutsch, Jan 23 2005
a(n) ~ A048651^2 * 2^(n*(n-1)/2). - Vaclav Kotesovec, Oct 09 2019
MAPLE
p:=proc(n) if n=0 then 1 else product(2^i-1, i=1..n) fi end: a:=n->p(n-1)*sum((-1)^j/p(j), j=0..n-1): seq(a(n), n=1..17); # Emeric Deutsch, Jan 23 2005
MATHEMATICA
a[1] = 1; a[n_] := a[n] = (2^(n-1)-1)*a[n-1] + (-1)^(n-1); Array[a, 15] (* Jean-François Alcover, Apr 05 2016, after Max Alekseyev *)
With[{q = 2}, Table[QFactorial[n, q] Sum[(-1)^k/QFactorial[k, q], {k, 0, n}], {n, 0, 20}]] (* Vladimir Reshetnikov, Sep 12 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Max Alekseyev, Apr 27 2010
STATUS
approved