A081047 Difference of Stirling numbers of the first kind.
1, 0, -1, -5, -26, -154, -1044, -8028, -69264, -663696, -6999840, -80627040, -1007441280, -13575738240, -196287356160, -3031488633600, -49811492505600, -867718162483200, -15974614352793600, -309920046408806400, -6320046028584960000
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..400
- Thierry Dana-Picard and David G. Zeitoun, Sequences of definite integrals, infinite series and Stirling numbers, International Journal of Mathematical Education in Science and Technology, Volume 43, 2012 - Issue 2.
- Motohico Mulase, In Search of a Hidden Curve, arXiv:2501.00716 [math.QA], 2025. See p. 27.
Programs
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Mathematica
With[{nn = 100}, CoefficientList[Series[(1 + Log[1 - x])/(1 - x), {x, 0, nn}], x] Range[0, nn]!] (* G. C. Greubel, Jan 21 2017 *)
Formula
E.g.f.: (1+log(1-x))/(1-x). - Paul Barry, Nov 26 2008
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)
a(n) = A094645(n+2,2), n>=0. - _Wolfdieter Lang, Jun 20 2011