A081052 Difference of Stirling numbers of the first kind.

0, 1, -4, 17, -85, 499, -3388, 26200, -227708, 2199276, -23382216, 271461816, -3418002432, 46399476096, -675622445184, 10504980616320, -173726527230720, 3045008035203840, -56389237652344320, 1100174877158791680, -22556707790402304000, 484876713643386624000

Offset: 0

Author

Paul Barry, Mar 05 2003

Keywords

• easy
• sign

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A000399, A081051, A081048.

Programs

Mathematica

Table[StirlingS1[n,2]-StirlingS1[n,3],{n,30}] (* Harvey P. Dale, May 02 2012 *)

PARI

for(n=1, 22, print1(stirling(n, 2) - stirling(n, 3),", ")) \\ Indranil Ghosh, Mar 11 2017

Formula

a(n) = s(n,2) - s(n,3), s(n,m) = signed Stirling number of the first kind.

E.g.f. (1+x)^-1 * (log(1+x) - (log(1+x)^2)/2).

Conjecture: a(n) +3*(n-1)*a(n-1) +(3*n^2-9*n+7)*a(n-2) +(n-2)^3*a(n-3)=0. - R. J. Mathar, Nov 24 2012