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Search: id:A128061
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| A128061 |
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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.). |
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+0
2
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| 1, -3, 37, -29, 2761, -97, -268271, 14759, 2804929, -9435089, 3731508001, 1185970223, -264025807957621, 44820288709817, 4570382525453089, -336032650312339, 23787999916667875201, 4316502548043120587, -4994567510209019657318207
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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FORMULA
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b(0)=1. b(n) = -sum{k=1 to n} binomial(n,k) H(k+1) b(n-k)/(k+1).
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EXAMPLE
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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 ...
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MATHEMATICA
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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]] (*Chandler*)
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CROSSREFS
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Cf. A128062.
Sequence in context: A073236 A002563 A140448 this_sequence A116184 A037000 A042333
Adjacent sequences: A128058 A128059 A128060 this_sequence A128062 A128063 A128064
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KEYWORD
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frac,sign
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AUTHOR
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Leroy Quet Feb 13 2007
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Feb 19 2007
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