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Search: id:A152668
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| A152668 |
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Number of runs of even entries in all permutations of {1,2,...,n} (the permutation 274831659 has 3 runs of even entries: 2, 48 and 6). |
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+0
2
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| 2, 6, 36, 192, 1440, 10800, 100800, 967680, 10886400, 127008000, 1676505600, 22992076800, 348713164800, 5492232345600, 94152554496000, 1673823191040000, 32011868528640000, 633834996867072000, 13380961044971520000
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OFFSET
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2,1
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COMMENT
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a(n)=Sum(k*A152667(n,k),k=1..floor(n/2)).
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FORMULA
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a(2n) = (n+1)(2n)!/2;
a(2n+1) = n(n+2)(2n)!
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EXAMPLE
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a(3)=6 because each of the permutations 123,132,213,231,312,321 has exactly 1 run of even entries.
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MAPLE
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ae := proc (n) options operator, arrow: (1/2)*factorial(2*n)*(n+1) end proc: ao := proc (n) options operator, arrow: n*(n+2)*factorial(2*n) end proc: a := proc (n) if `mod`(n, 2) = 0 then ae((1/2)*n) else ao((1/2)*n-1/2) end if end proc; seq(a(n), n = 2 .. 20);
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CROSSREFS
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A152667, A052618.
Sequence in context: A130874 A019020 A101609 this_sequence A086325 A074424 A002868
Adjacent sequences: A152665 A152666 A152667 this_sequence A152669 A152670 A152671
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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 14 2008
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