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A155519
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a(n) = Sum (J(p): p is a permutation of {1,2,...,n}), where J(p) is the number of j <=ceil(n/2) such that p(j)+p(n+1-j)=n+1.
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2
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1, 2, 4, 16, 72, 432, 2880, 23040, 201600, 2016000, 21772800, 261273600, 3353011200, 46942156800, 697426329600, 11158821273600, 188305108992000, 3389491961856000, 64023737057280000, 1280474741145600000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n)=Sum(k*A155517(n,k),k=0..ceil(n/2)).
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FORMULA
| a(2n-1)=n(2n-2)!; a(2n)=2(2n-2)!*n^2.
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EXAMPLE
| a(3)=4 because J(123)=2 (counting j=1,2), J(321)=2 (counting j=1,2) and J(132)=J(312)=J(213)=J(231)=0.
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MAPLE
| a := proc (n) if `mod`(n, 2) = 1 then (1/2)*(n+1)*factorial(n-1) else (1/2)*factorial(n-2)*n^2 end if end proc: seq(a(n), n = 1 .. 23);
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CROSSREFS
| A155517, A155518.
Sequence in context: A061652 A162119 A192623 * A180391 A058926 A102736
Adjacent sequences: A155516 A155517 A155518 * A155520 A155521 A155522
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 26 2009
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