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 A118050 Numerators of coefficients in a series for the inverse of harmonic number H(x). 3
 1, -1, 3, -1525, 615881, -3058641, 38800188510523, -3213747182969063, 100462329712125, -43865443313064357090353257, 4543042335221166932765440567147, -103986681387361620043171941 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..11. David W. Cantrell, Inverse of Harmonic Numbers EXAMPLE 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. MATHEMATICA n = 12; coeffs = InverseSeries[Exp[Series[HarmonicNumber[x - 1/2], {x, Infinity, 2n - 1}] - EulerGamma]][[3]]; Table[Numerator[coeffs[[2i - 1]]], {i, 1, n}] CROSSREFS Denominators given in A118051. See also A002387. Sequence in context: A264427 A285656 A239503 * A246637 A302132 A346653 Adjacent sequences: A118047 A118048 A118049 * A118051 A118052 A118053 KEYWORD frac,sign AUTHOR David W. Cantrell (DWCantrell(AT)sigmaxi.net), Apr 08 2006 STATUS approved

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Last modified June 2 15:42 EDT 2023. Contains 363098 sequences. (Running on oeis4.)