%I A092186
%S A092186 2,1,2,2,8,12,72,144,1152,2880,28800,86400,1036800,3628800,50803200,203212800,
%T A092186 3251404800,14631321600,263363788800,1316818944000,26336378880000,144850083840000,
%U A092186 3186701844480000,19120211066880000,458885065605120000,2982752926433280000
%N A092186 a(n) = 2(m!)^2 for n = 2m and m!(m+1)! for n = 2m+1.
%C A092186 Singmaster's problem: "A salesman's office is located on a straight road. 
               His n customers are all located along this road to the east of the 
               office, with the office of customer k at distance k from the salesman's 
               office. The salesman must make a driving trip whereby he leaves the 
               office, visits each customer exactly once, then returns to the office.
%C A092186 "Because he makes a profit on his mileage allowance, the salesman wants 
               to drive as far as possible during his trip. What is the maximum 
               possible distance he can travel on such a trip and how many different 
               such trips are there?
%C A092186 "Assume that if the travel plans call for the salesman to visit customer 
               j immediately after he visits customer i, then he drives directly 
               from i to j."
%C A092186 The solution to the first question is twice A002620(n-1); the solution 
               to the second question is a(n).
%C A092186 Number of permutation of [n] with no pair of consecutive elements of 
               the same parity. - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 26 
               2007
%D A092186 David Singmaster, Problem 1654, Mathematics Magazine 75 (October 2002). 
               Solution in Mathematics Magazine 76 (October 2003).
%Y A092186 Sequence in context: A145859 A145863 A110775 this_sequence A138262 A127510 
               A158810
%Y A092186 Adjacent sequences: A092183 A092184 A092185 this_sequence A092187 A092188 
               A092189
%K A092186 nonn
%O A092186 0,1
%A A092186 N. J. A. Sloane (njas(AT)research.att.com), based on correspondence from 
               Hugo Pfoertner and Rob Pratt, Apr 02 2004