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 A051684 Auxiliary sequence for calculation of number of even permutations of degree n and order exactly 2. 2

%I

%S 0,-1,-3,-3,5,15,-21,-133,27,1215,935,-12441,-23673,138047,469455,

%T -1601265,-9112561,18108927,182135007,-161934625,-3804634785,

%U -404007681,83297957567

%N Auxiliary sequence for calculation of number of even permutations of degree n and order exactly 2.

%D V. Jovovic, Some combinatorial characteristics of symmetric and alternating groups (in Russian), Belgrade, 1980, unpublished.

%F a(n) = c(n, 2), where c(n, d)=Sum_{k=1..n} (-1)^(k+1)*(n-1)!/(n-k)! *Sum_{l:lcm{k, l}=d} c(n-k, l), c(0, 1)=1.

%F a(n)=2*A048099(n)-A001189(n)=A048099(n)-A001465(n) a(n)=(-1)^n*A001464(n)-1 a(n)=a(n-1)-(n-1)*(a(n-2)+1) E.g.f.: -e^x+e^(x-(1/2)*x^2) - Matthew J. White (mattjameswhite(AT)hotmail.com), Mar 02 2006

%F a(n) = Sum((-1)^j*n!/(2^j*j!*(n-2*j)!),j=1..floor(n/2)). - _Vladeta Jovovic_, Mar 06 2006

%Y Cf. A001189, A051685.

%K sign

%O 1,3