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%I M0923 N0347 #28 Aug 02 2015 20:23:18
%S 1,2,3,26,13,1074,-1457,61802,7929,4218722,-6385349,934344762,
%T -5065189307,141111736466,235257551943,23219206152074,-97011062913167,
%U 11887164842925762,-91890238533000461,4819930221202545242,-14547510704199530499,1184314832978574919922
%N Sum of logarithmic numbers.
%D J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H J. M. Gandhi, <a href="/A002741/a002741.pdf">On logarithmic numbers</a>, Math. Student, 31 (1963), 73-83. [Annotated scanned copy]
%H <a href="/index/Lo#logarithmic">Index entries for sequences related to logarithmic numbers</a>
%F E.g.f.: F(x)/exp(x)/x where F(x) is o.g.f. for A000203(). - _Vladeta Jovovic_, Feb 09 2003
%p 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
%t 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_ *)
%Y Cf. A002750.
%K sign,easy
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Jeffrey Shallit_
%E More terms from _R. J. Mathar_, Oct 22 2007
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