A002748 Sum of logarithmic numbers. (Formerly M0923 N0347)

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

Offset

0,2

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

Table of n, a(n) for n=0..21.

J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83. [Annotated scanned copy]

Index entries for sequences related to logarithmic numbers

Formula

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

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 *)

Crossrefs

Cf. A002750.

Sequence in context: A060371 A358390 A130975 * A056004 A032812 A099006

Adjacent sequences: A002745 A002746 A002747 * A002749 A002750 A002751

Keyword

sign,easy

Author

N. J. A. Sloane

Extensions

More terms from Jeffrey Shallit

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

Status

approved