A081103 Alternating sum of first three Stirling numbers of the first kind.

0, 1, -4, 18, -95, 584, -4123, 32969, -294992, 2922956, -31791716, 376719892, -4832017320, 66713229192, -986611705584, 15561976320144, -260804276106624, 4628322010931328, -86710491660063744, 1710290952899283456, -35427639035553292800, 768970029545198092800

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = s(n, 1)-s(n, 2)+s(n, 3), s(n, m)= signed Stirling numbers of the first kind. E.g.f. (1+x)^(-1)*(log(1+x)-log(1+x)^2/2+log(1+x)^3/6

Crossrefs

Cf. A000399, A081052, A081046.

Sequence in context: A259533 A305239 A370344 * A243325 A005777 A180567

Adjacent sequences: A081100 A081101 A081102 * A081104 A081105 A081106

Keyword

easy,sign

Author

Paul Barry, Mar 05 2003

Status

approved