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

0, -1, -3, -3, 5, 15, -21, -133, 27, 1215, 935, -12441, -23673, 138047, 469455, -1601265, -9112561, 18108927, 182135007, -161934625, -3804634785, -404007681, 83297957567

Offset: 1

Author

Vladeta Jovovic

Keywords

• sign

References

• V. Jovovic, Some combinatorial characteristics of symmetric and alternating groups (in Russian), Belgrade, 1980, unpublished.

Crossrefs

Cf. A001189, A051685.

Formula

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.

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

a(n) = Sum((-1)^j*n!/(2^j*j!*(n-2*j)!),j=1..floor(n/2)). - Vladeta Jovovic, Mar 06 2006