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 A128061 a(n) = numerator of b(n), where sum{m>=0} b(m)*x^m/m! = x/(sum(m>=1} H(m) x^m/m!) = exp(-x)*x/(sum{m>=1} x^m (-1)^(m+1)/(m!*m)). (H(m) = sum{k=1 to m} 1/k.). 1
 1, -3, 37, -29, 2761, -97, -268271, 14759, 2804929, -9435089, 3731508001, 1185970223, -264025807957621, 44820288709817, 4570382525453089, -336032650312339, 23787999916667875201, 4316502548043120587, -4994567510209019657318207 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA b(0)=1. b(n) = -sum{k=1 to n} binomial(n,k) H(k+1) b(n-k)/(k+1). EXAMPLE 1/(1 + x * 3/(2 * 2) + x^2 * 11/(6 * 6) + x^3 * 25/(12 * 24) +...) = 1 -x * 3/4 + x^2 * 37/72 -x^3 * 29/96 ... MATHEMATICA b[0] = 1; b[n_] := b[n] = -Sum[Binomial[n, k] *HarmonicNumber[k + 1]*b[n - k]/(k + 1), {k, n}]; Numerator[Array[b, 20, 0]] (* Ray Chandler, Feb 19 2007 *) CROSSREFS Cf. A128062. Sequence in context: A073236 A002563 A140448 * A176240 A116184 A037000 Adjacent sequences:  A128058 A128059 A128060 * A128062 A128063 A128064 KEYWORD frac,sign AUTHOR Leroy Quet, Feb 13 2007 EXTENSIONS Extended by Ray Chandler, Feb 19 2007 STATUS approved

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Last modified July 23 22:20 EDT 2021. Contains 346265 sequences. (Running on oeis4.)