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A152875 Number of permutations of {1,2,...,n} (n>=2) with all odd entries preceding all even entries or all even entries preceding all odd entries. 1
2, 4, 8, 24, 72, 288, 1152, 5760, 28800, 172800, 1036800, 7257600, 50803200, 406425600, 3251404800, 29262643200, 263363788800, 2633637888000, 26336378880000, 289700167680000, 3186701844480000, 38240422133760000 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

a(n) = A152874(n,1).

LINKS

Table of n, a(n) for n=2..23.

FORMULA

a(2n) = 2n!^2; a(2n+1) = 2n!(n+1)!.

E.g.f. = 2(4sqrt(4-x^2)*arcsin(x/2)-4x+4x^2+x^3-x^4)/((2+x)(2-x)^2).

EXAMPLE

a(4)=8 because we have 1324, 1342, 3124, 3142, 2413, 2431, 4213 and 4231.

MAPLE

a := proc (n) if `mod`(n, 2) = 0 then 2*factorial((1/2)*n)^2 else 2*factorial((1/2)*n-1/2)*factorial((1/2)*n+1/2) end if end proc: seq(a(n), n = 2 .. 25);

CROSSREFS

Cf. A152874.

Sequence in context: A026097 A264557 A067646 * A179190 A291482 A065654

Adjacent sequences:  A152872 A152873 A152874 * A152876 A152877 A152878

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Dec 15 2008

STATUS

approved

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Last modified April 26 03:37 EDT 2019. Contains 322469 sequences. (Running on oeis4.)