A051685 Auxiliary sequence for calculation of number of even permutations of degree n and order exactly 4.

0, 0, 0, -6, -30, 0, 420, 2100, 6804, -20160, -376200, -2102760, -6606600, 53237184, 965306160, 5941244400, 12774059760, -305998041600, -5264368533216, -33983490935520, -16008359119200, 3139364813249280, 52132631033313600, 341037535726730304, -715693892444414400

Offset: 1

Author

Vladeta Jovovic

Keywords

• easy
• sign

References

• V. Jovovic, Some combinatorial characteristics of symmetric and alternating groups (in Russian), Belgrade, 1980, unpublished.

Crossrefs

Cf. A001189, A001473, A051684.

Formula

a(n) = c(n, 4), 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.

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 05 2003