OFFSET
0,2
COMMENTS
Previous name was: A simple grammar.
a(n) is the number of ways to seat n people at circular tables, then linearly order the tables, then designate some (possibly all or none) of the tables at which only one person is seated. a(2) = 9 because we have: (1)(2), (1')(2), (1)(2'), (1')(2'), (2)(1), (2')(1), (2)(1'), (2')(1'), (1,2). Cf. A007840. - Geoffrey Critzer, Nov 05 2013
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..395
W. S. Gray and M. Thitsa, System Interconnections and Combinatorial Integer Sequences, in: System Theory (SSST), 2013 45th Southeastern Symposium on, Date of Conference: 11-11 Mar 2013.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 785
Makhin Thitsa and W. Steven Gray, On the Radius of Convergence of Cascaded Analytic Nonlinear Systems, 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), Orlando, FL, USA, December 12-15, 2011, pp. 3830-3835.
M. Thitsa and W. S. Gray, On the radius of convergence of cascaded analytic nonlinear systems: The SISO case, System Theory (SSST), 2011 IEEE 43rd Southeastern Symposium on, 14-16 March 2011, pp. 30-36.
Makhin Thitsa and W. Steven Gray, On the Radius of Convergence of Interconnected Analytic Nonlinear Input-Output Systems, SIAM Journal on Control and Optimization, Vol. 50, No. 5, 2012, pp. 2786-2813. - From N. J. A. Sloane, Dec 26 2012
FORMULA
E.g.f.: -1/(-1+x+log(-1/(-1+x))).
a(n) ~ n! * (1/(1-LambertW(1)))^n/(1/LambertW(1)-LambertW(1)). - Vaclav Kotesovec, Oct 01 2013
a(0) = 1; a(n) = n * a(n-1) + Sum_{k=0..n-1} binomial(n,k) * (n-k-1)! * a(k). - Ilya Gutkovskiy, Apr 26 2021
MAPLE
spec := [S, {C=Cycle(Z), B=Union(C, Z), S=Sequence(B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
CoefficientList[Series[1/(1-x+Log[1-x]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 01 2013 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
New name using e.g.f., Vaclav Kotesovec, Oct 01 2013
STATUS
approved