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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 FORMULA a(2n) = 2n!^2; a(2n+1) = 2n!(n+1)!. E.g.f. = 2*(4*sqrt(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 May 7 10:46 EDT 2021. Contains 343650 sequences. (Running on oeis4.)