

A092186


a(n) = 2(m!)^2 for n = 2m and m!(m+1)! for n = 2m+1.


9



2, 1, 2, 2, 8, 12, 72, 144, 1152, 2880, 28800, 86400, 1036800, 3628800, 50803200, 203212800, 3251404800, 14631321600, 263363788800, 1316818944000, 26336378880000, 144850083840000, 3186701844480000, 19120211066880000, 458885065605120000, 2982752926433280000
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OFFSET

0,1


COMMENTS

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.
"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?
"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."
The solution to the first question is twice A002620(n1); the solution to the second question is a(n).
Number of permutation of [n] with no pair of consecutive elements of the same parity.  Vladeta Jovovic, Nov 26 2007


REFERENCES

A. O. Munagi, Alternating subsets and permutations, Rocky Mountain J. Math. 40 (6) (2010) 19651977 doi:10.1216/RJM20104061965, Corollary 3.2.
David Singmaster, Problem 1654, Mathematics Magazine 75 (October 2002). Solution in Mathematics Magazine 76 (October 2003).


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..300
David Singmaster, Problem 1654, Mathematics Magazine 75 p. 317 (October 2002). Solution, Mathematics Magazine 76 p. 321322 (October 2003).
Shinji Tanimoto, Alternate Permutations and Signed Eulerian Numbers, arXiv:math/0612135 [math.CO], 2006; Ann. Comb. 14 (2010), 355.


MAPLE

a:= proc(n) option remember; `if`(n<2, 2n,
(n*(3*n1)*(n1)*a(n2) 4*a(n1))/(12*n16))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Nov 11 2013


MATHEMATICA

f[n_] := If[EvenQ[n], 2 (n/2)!^2, ((n + 1)/2)! ((n  1)/2)!]; Table[
f[n], {n, 0, 25}] (* Geoffrey Critzer, Aug 24 2013 *)


CROSSREFS

Cf. A152877.
Row sums of A125300.  Alois P. Heinz, Nov 18 2013
Sequence in context: A240492 A110775 A229232 * A138262 A276990 A127510
Adjacent sequences: A092183 A092184 A092185 * A092187 A092188 A092189


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, based on correspondence from Hugo Pfoertner and Rob Pratt, Apr 02 2004


STATUS

approved



