OFFSET
0,2
COMMENTS
Previous name was: A simple grammar.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 818
FORMULA
E.g.f.: (-x-log((-1+x)/(-1+2*x))+log((-1+x)/(-1+2*x))*x)/(-1+x).
Recurrence: {a(1)=2, a(2)=5, a(3)=20, a(4)=114, (2*n^3-2*n)*a(n)+(-3*n^2+2*n+5)*a(n+1)+(-2+n)*a(n+2)}.
For n>0, a(n) = (n-1)! * (2^n+n-1). - Vaclav Kotesovec, Oct 01 2013
MAPLE
spec := [S, {B=Sequence(Z, 1 <= card), C=Cycle(B), S=Union(B, C)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
a:= n-> `if`(n=0, 0, (2^n+n-1)*(n-1)!): seq(a(n), n=0..25); # Alois P. Heinz, Nov 09 2011
MATHEMATICA
CoefficientList[Series[x/(1-x)+Log[(1-x)/(1-2*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