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Search: id:A152875
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| A152875 |
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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. |
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+0
2
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| 2, 4, 8, 24, 72, 288, 1152, 5760, 28800, 172800, 1036800, 7257600, 50803200, 406425600, 3251404800, 29262643200, 263363788800, 2633637888000, 26336378880000, 289700167680000, 3186701844480000, 38240422133760000
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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a(n)=A152874(n,1).
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FORMULA
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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]
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EXAMPLE
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a(4)=8 because we have 1324, 1342, 3124, 3142, 2413, 2431, 4213 and 4231.
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MAPLE
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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);
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CROSSREFS
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A152874
Sequence in context: A115115 A026097 A067646 this_sequence A065654 A002908 A004528
Adjacent sequences: A152872 A152873 A152874 this_sequence A152876 A152877 A152878
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 15 2008
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