%I A118050
%S A118050 1,1,3,1525,615881,3058641,38800188510523,3213747182969063,
%T A118050 100462329712125,43865443313064357090353257,
%U A118050 4543042335221166932765440567147,103986681387361620043171941
%V A118050 1,-1,3,-1525,615881,-3058641,38800188510523,-3213747182969063,100462329712125,
%W A118050 -43865443313064357090353257,4543042335221166932765440567147,
%X A118050 -103986681387361620043171941
%N A118050 Numerators of coefficients in a series for the inverse of harmonic number 
               H(x).
%H A118050 David W. Cantrell, <a href="http://groups.google.com/group/sci.math/msg/
               0926db8773d69b81">Inverse of Harmonic Numbers</a>
%e A118050 With InvH(x) being the inverse of H(x), x > 0, an asymptotic series for 
               InvH(x) + 1/2 is u - 1/(24u) + 3/(640u^3) - 1525/(580608u^5) +-... 
               where u = e^(x - g) and g is Euler's gamma constant.
%t A118050 n = 12; coeffs = InverseSeries[Exp[Series[HarmonicNumber[x - 1/2], {x, 
               Infinity, 2n - 1}] - EulerGamma]][[3]]; Table[Numerator[coeffs[[2i 
               - 1]]], {i, 1, n}]
%Y A118050 Denominators given in A118051. See also A002387.
%Y A118050 Sequence in context: A036066 A060307 A119111 this_sequence A116994 A096730 
               A024047
%Y A118050 Adjacent sequences: A118047 A118048 A118049 this_sequence A118051 A118052 
               A118053
%K A118050 frac,sign
%O A118050 0,3
%A A118050 David W. Cantrell (DWCantrell(AT)sigmaxi.net), Apr 08 2006