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A002749 Sum of logarithmic numbers.

%I A002749 M4767 N2037 #27 Oct 20 2023 09:39:05
%S A002749 1,1,1,11,-7,389,-1031,19039,-24431,1023497,-4044079,225738611,
%T A002749 -1711460279,29974303501,4656373513,3798866053319,-34131041040991,
%U A002749 2131052083901969,-23678368533941471,832900320313739227,-4752766287768240359,148482851420849206421
%N A002749 Sum of logarithmic numbers.
%D A002749 J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83.
%D A002749 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002749 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002749 J. M. Gandhi, <a href="/A002741/a002741.pdf">On logarithmic numbers</a>, Math. Student, 31 (1963), 73-83. [Annotated scanned copy]
%H A002749 <a href="/index/Lo#logarithmic">Index entries for sequences related to logarithmic numbers</a>
%F A002749 E.g.f.: F(x)/exp(x)/x where F(x) is o.g.f. for A000005(). - _Vladeta Jovovic_, Feb 09 2003
%p A002749 A002749 := proc(r)
%p A002749     add(A260324(n,r),n=1..r+1) ;
%p A002749 end proc:
%p A002749 seq(A002749(r),r=0..25) ; # _R. J. Mathar_, Jul 24 2015
%t A002749 m = 22;
%t A002749 F[x_] = Sum[DivisorSigma[0, n] x^n , {n, 1, m}];
%t A002749 CoefficientList[F[x]/(x E^x) + O[x]^m, x] Range[0, m-1]! (* _Jean-François Alcover_, Mar 30 2020 *)
%K A002749 sign
%O A002749 0,4
%A A002749 _N. J. A. Sloane_
%E A002749 Corrected and extended by _Jeffrey Shallit_