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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 (list; graph; refs; listen; history; text; internal format)
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(n-1); 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

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

MAPLE

a:= proc(n) option remember; `if`(n<2, 2-n,

      (n*(3*n-1)*(n-1)*a(n-2) -4*a(n-1))/(12*n-16))

    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 A127510 A158810

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

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Last modified April 18 11:01 EDT 2014. Contains 240707 sequences.