A002748 Sum of logarithmic numbers.

1, 2, 3, 26, 13, 1074, -1457, 61802, 7929, 4218722, -6385349, 934344762, -5065189307, 141111736466, 235257551943, 23219206152074, -97011062913167, 11887164842925762, -91890238533000461, 4819930221202545242, -14547510704199530499, 1184314832978574919922

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• easy

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

Crossrefs

Cf. A002750.

Programs

Maple

A002748 := proc(n) local f1,f2 ; f1 := add(numtheory[sigma](i)*x^(i-1),i=1..n+1) ; f2 := add((-x)^i/i!,i=0..n+1) ; n!*coeftayl(f1*f2,x=0,n) ; end: seq(A002748(n),n=0..25) ; # R. J. Mathar, Oct 22 2007

Mathematica

f1[n_] := Sum[DivisorSigma[1, i]*x^(i-1), {i, 1, n+1}]; f2[n_] := Sum[(-x)^i/i!, {i, 0, n+1}] ; a[n_] := n!*SeriesCoefficient[f1[n]*f2[n], {x, 0, n}]; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Jan 17 2014, after R. J. Mathar *)

Formula

E.g.f.: F(x)/exp(x)/x where F(x) is o.g.f. for A000203(). - Vladeta Jovovic, Feb 09 2003

Extensions

More terms from Jeffrey Shallit

More terms from R. J. Mathar, Oct 22 2007