OFFSET
0,3
COMMENTS
Previous name was: A simple grammar.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..360
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 819
FORMULA
E.g.f.: 1/2 - (1/2)*(1-4*log(-1/(-1+x)))^(1/2).
a(n) = Sum_{k=1..n} Stirling1(n,k)*k!*C(2*k-2,k-1)/k*(-1)^(n+k). - Vladimir Kruchinin, May 12 2012
a(n) ~ n^(n-1)/(sqrt(2)*exp(3*n/4)*(exp(1/4)-1)^(n-1/2)). - Vaclav Kotesovec, Sep 30 2013
From Seiichi Manyama, Sep 09 2024: (Start)
E.g.f. satisfies A(x) = (-log(1 - x)) / (1 - A(x)).
E.g.f.: Series_Reversion( 1 - exp(-x * (1 - x)) ). (End)
MAPLE
spec := [S, {B=Cycle(Z), S=Prod(B, C), C=Sequence(S)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
CoefficientList[Series[1/2-1/2*(1+4*Log[1-x])^(1/2), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 30 2013 *)
PROG
(Maxima) a(n):=sum(stirling1(n, k)*k!*binomial(2*k-2, k-1)/k*(-1)^(n+k), k, 1, n); /* Vladimir Kruchinin, May 12 2012 */
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
New name using e.g.f., Vaclav Kotesovec, Sep 30 2013
STATUS
approved