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Search: id:A152886
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| A152886 |
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Number of descents beginning and ending with an even number in all permutations of {1,2,...,n}. |
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+0
3
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| 0, 0, 0, 6, 24, 360, 2160, 30240, 241920, 3628800, 36288000, 598752000, 7185024000, 130767436800, 1830744115200, 36614882304000, 585838116864000, 12804747411456000, 230485453406208000, 5474029518397440000
(list; graph; listen)
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OFFSET
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1,4
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FORMULA
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a(2n)=(2n-1)!*binom(n,2); a(2n+1)=(2n)!*binom(n,2).
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EXAMPLE
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a(7)=2160 because (i) the descent pairs can be chosen in binom(3,2)=3 ways, namely (4,2), (6,2), (6,4); (ii) they can be placed in 6 positions, namely (1,2),(2,3),(3,4),(4,5),(5,6),(6,7); (iii) the remaining 5 entries can be permuted in 5!=120 ways; 3*6*120=2160.
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MAPLE
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a := proc (n) if `mod`(n, 2) = 0 then factorial(n-1)*binomial((1/2)*n, 2) else factorial(n-1)*binomial((1/2)*n-1/2, 2) end if end proc: seq(a(n), n = 1 .. 22);
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CROSSREFS
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A152885, A152887
Sequence in context: A052733 A010567 A097171 this_sequence A128614 A139240 A052524
Adjacent sequences: A152883 A152884 A152885 this_sequence A152887 A152888 A152889
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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), Jan 19 2009
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