update to A094047: arrangements of n couples

Max Alekseyev maxale at gmail.com
Mon Feb 11 07:09:07 CET 2008

```Neil, SeqFans,

I propose the following update to A094047 based on the formula that
I've got for its terms.

Regards,
Max

%I A094047
%S A094047 0,0,2,12,312,9600,416880,23879520,1749363840,159591720960,17747520940800,2363738855385600,
%T A094047 371511874881100800,68045361697964851200,14367543450324474009600,3464541314885011705344000,
%U A094047 946263209467217020194816000,290616691739323132839591936000,99714530592486301158487941120000
%N A094047 Number of arrangements of n couples around a round table so
that each person sits between two people of the opposite gender and no
couple is seated together.
%F A094047 For n>1, a(n) = (-1)^n * 2 * (n-1)! + n! * SUM[j=0..n-1]
(-1)^j * (n-j-1)! * binomial(2*n-j-1,j).
%C A094047 Also, the number of Hamiltonian directed circuits in the
crown graph of order n.
%H A094047 Eric Weisstein's World of Mathematics, <a
href="http://mathworld.wolfram.com/CrownGraph.html">Crown Graph</a>
%H A094047 Eric Weisstein's World of Mathematics, <a
href="http://mathworld.wolfram.com/HamiltonianCircuit.html">Hamiltonian
Circuit</a>
%Y A094047 Cf. A114939, A137729.
%Y A094047 Adjacent sequences: A094044 A094045 A094046 this_sequence
A094048 A094049 A094050
%Y A094047 Sequence in context: A012425 A012422 A122767 this_sequence
A091472 A012727 A088229
%K A094047 nonn
%O A094047 1,3
%A A094047 Matthijs Coster (matthijs(AT)coster.demon.nl), Apr 29 2004
%E A094047 Better definition from Joel Lewis
(jblewis(AT)post.harvard.edu), Jun 30 2007
%E A094047 Formula and further terms from Max Alekseyev
(maxal(AT)cs.ucsd.edu), Feb 10 2008

```