A002749 Sum of logarithmic numbers.

1, 1, 1, 11, -7, 389, -1031, 19039, -24431, 1023497, -4044079, 225738611, -1711460279, 29974303501, 4656373513, 3798866053319, -34131041040991, 2131052083901969, -23678368533941471, 832900320313739227, -4752766287768240359, 148482851420849206421

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

References

• J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83. [Annotated scanned copy]
• Index entries for sequences related to logarithmic numbers

Programs

Maple

A002749 := proc(r)
    add(A260324(n,r),n=1..r+1) ;
end proc:
seq(A002749(r),r=0..25) ; # R. J. Mathar, Jul 24 2015

Mathematica

m = 22;
F[x_] = Sum[DivisorSigma[0, n] x^n , {n, 1, m}];
CoefficientList[F[x]/(x E^x) + O[x]^m, x] Range[0, m-1]! (* Jean-François Alcover, Mar 30 2020 *)

Formula

E.g.f.: F(x)/exp(x)/x where F(x) is o.g.f. for A000005(). - Vladeta Jovovic, Feb 09 2003

Extensions

Corrected and extended by Jeffrey Shallit