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A077613 Number of adjacent pairs of form (even,odd) among all permutations of {1,2,...,n}. Also, number of adjacent pairs of form (odd,even). 8
0, 1, 4, 24, 144, 1080, 8640, 80640, 806400, 9072000, 108864000, 1437004800, 20118067200, 305124019200, 4881984307200, 83691159552000, 1506440871936000, 28810681675776000, 576213633515520000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..449

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.

a(n) = A002620(n) * A000142(n-1). - Michel Marcus, Aug 29 2013

MATHEMATICA

Array[Floor[#/2] Ceiling[#/2] (# - 1)! &, 19] (* Michael De Vlieger, Aug 16 2017 *)

PROG

(PARI) a(n) = floor(n/2)*ceil(n/2)*(n-1)!; \\ Michel Marcus, Aug 29 2013

CROSSREFS

Cf. A077611, A077612.

Sequence in context: A067411 A045915 A052609 * A072949 A104531 A225050

Adjacent sequences:  A077610 A077611 A077612 * A077614 A077615 A077616

KEYWORD

nonn

AUTHOR

Leroy Quet, Frank Ruskey and Dean Hickerson, Nov 11 2002

STATUS

approved

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Last modified May 9 00:09 EDT 2021. Contains 343685 sequences. (Running on oeis4.)