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A077613
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Number of adjacent pairs of form (even,odd) among all permutations of {1,2,...,n}. Also, number of adjacent pairs of form (odd,even).
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5
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0, 1, 4, 24, 144, 1080, 8640, 80640, 806400, 9072000, 108864000, 1437004800, 20118067200, 305124019200, 4881984307200, 83691159552000, 1506440871936000, 28810681675776000, 576213633515520000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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FORMULA
| a(n) = floor(n/2)*ceiling(n/2)*(n-1)!. Proof: There are floor(n/2)*ceiling(n/2) pairs (r, s) with r even and s odd. For each pair, there are n-1 places it can occur in a permutation and (n-2)! possible arrangements of the other numbers.
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CROSSREFS
| Cf. A077611, A077612.
Sequence in context: A067411 A045915 A052609 * A072949 A104531 A045738
Adjacent sequences: A077610 A077611 A077612 * A077614 A077615 A077616
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Frank Ruskey (ruskey(AT)cs.uvic.ca) and Dean Hickerson (dean.hickerson(AT)yahoo.com), Nov 11 2002
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