A081047 - OEIS

%I #17 Jan 22 2017 21:54:16

%S 1,0,-1,-5,-26,-154,-1044,-8028,-69264,-663696,-6999840,-80627040,

%T -1007441280,-13575738240,-196287356160,-3031488633600,

%U -49811492505600,-867718162483200,-15974614352793600,-309920046408806400,-6320046028584960000

%N Difference of Stirling numbers of the first kind.

%H G. C. Greubel, <a href="/A081047/b081047.txt">Table of n, a(n) for n = 0..400</a>

%H Thierry Dana-Picard and David G. Zeitoun, <a href="http://dx.doi.org/10.1080/0020739X.2011.582172">Sequences of definite integrals, infinite series and Stirling numbers</a>, International Journal of Mathematical Education in Science and Technology, Volume 43, 2012 - Issue 2.

%F E.g.f.: (1+log(1-x))/(1-x). - _Paul Barry_, Nov 26 2008

%F a(n) = abs(s(n+1, 1))-abs(s(n+1, 2)), where s(n, m) is a (signed) Stirling number of the first kind (A008275). (corrected by _Wolfdieter Lang_, Jun 20 2011)

%F a(n) = A094645(n+2,2), n>=0. - _Wolfdieter Lang, Jun 20 2011

%t With[{nn = 100}, CoefficientList[Series[(1 + Log[1 - x])/(1 - x), {x, 0, nn}], x] Range[0, nn]!] (* _G. C. Greubel_, Jan 21 2017 *)

%Y Cf. A001705, A008275, A081046.

%K easy,sign

%O 0,4

%A _Paul Barry_, Mar 05 2003