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 A077612 Number of adjacent pairs of form (even,even) among all permutations of {1,2,...,n}. 3

%I

%S 0,0,0,12,48,720,4320,60480,483840,7257600,72576000,1197504000,

%T 14370048000,261534873600,3661488230400,73229764608000,

%U 1171676233728000,25609494822912000,460970906812416000

%N Number of adjacent pairs of form (even,even) among all permutations of {1,2,...,n}.

%F 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.

%F a(n) = A110660(n+2) * A000142(n-1). - _Michel Marcus_, Aug 29 2013

%o (PARI) a(n) = n\2 * (n\2-1)*(n-1)! ; \\ _Michel Marcus_, Aug 29 2013

%Y Cf. A077611, A077613.

%K nonn

%O 1,4

%A _Leroy Quet_, _Frank Ruskey_ and _Dean Hickerson_, Nov 11 2002

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