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A077612
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Number of adjacent pairs of form (even,even) among all permutations of {1,2,...,n}.
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3
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0, 0, 0, 12, 48, 720, 4320, 60480, 483840, 7257600, 72576000, 1197504000, 14370048000, 261534873600, 3661488230400, 73229764608000, 1171676233728000, 25609494822912000, 460970906812416000, 10948059036794880000, 218961180735897600000, 5620003638888038400000
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OFFSET
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1,4
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LINKS
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FORMULA
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a(n) = floor(n/2)*floor(n/2-1)*(n-1)!. Proof: There are floor(n/2)*floor(n/2-1) pairs (r, s) with r and s even and distinct. 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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MATHEMATICA
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a[n_] := Floor[n/2]*Floor[n/2 - 1]*(n - 1)!; Array[a, 25] (* Amiram Eldar, Jan 22 2023 *)
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PROG
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(PARI) a(n) = n\2 * (n\2-1)*(n-1)! ; \\ Michel Marcus, Aug 29 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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