1,1

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, pg 66 (2.1.27,29).

Alexsandar Petojevic, The Function vM_m(s; a; z) and Some Well-Known Sequences, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7

Index entries for sequences related to necklaces

a(n)=(n-1)!*2^n. E.g.f.: log(1/(1-2x)).

Let gd(x,n)=Diff(exp(-(1/2)*x^2)*sqrt(2)/(2*sqrt(Pi)), x$n)]=(-1)^((1/2)*n)*(x^2)^((1/2)*n)*2^(-(1/2)*n+1/2)*(exp(I*Pi*n)+1)/(4*sqrt(Pi)*GAMMA(1+(1/2)*n)) be the n-th derivative of the standard Gaussian distribution. Evaluating gd(x,n) at x=1 gives gd(1,n)=2^(-(1/2)*n+1/2)*(exp(I*Pi*n)+1)*(-1)^((1/2)*n)/(4*sqrt(Pi)*GAMMA(1+(1/2)*n)). A066318 is the denominator of the even summands of the taylor series expansion of the Gaussian distribution evaluated at x=1. A066318[n]=denom(gd(1, 2*n))/sqrt(Pi) [From Stephen Crowley (crow(AT)crowlogic.net), May 16 2009]

seq(count(Permutation(n))*count(Subset(n+1)), n=0..17); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 16 2006

with(combstruct):A:=[N, {N=Cycle(Union(Z$2))}, labeled]: seq(count(A, size=n), n=1..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 07 2007

Apart from initial term, same as A032184.

Sequence in context: A009565 A009838 A088335 this_sequence A066952 A135249 A110365

Adjacent sequences: A066315 A066316 A066317 this_sequence A066319 A066320 A066321

nonn

Christian G. Bower (bowerc(AT)usa.net), Dec 13 2001

Added formula involving Gaussian series expansion [From Stephen Crowley (crow(AT)crowlogic.net), May 16 2009]