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A089963
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a(n) = Taylor coefficient at x=li(e) of the inverse of the function li(x) (the logarithm integral) multiplied by exp(n).
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2
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1, 0, -1, 2, 1, -26, 99, 90, -3627, 21054, 21735, -1465278, 11769033, 10145862, -1292734485, 13592476842, 5651236989, -2114795158962, 28081762413807, -8040489684078, -5763467251713423, 94263221264053590, -115569462262872717, -24259606258553011206, 479901663461939425317
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OFFSET
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1,4
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COMMENTS
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Define the inverse of li(x) by H(z) and the point Zo = li(e). Then H(z)= e + a(1)*exp(-1)*(z-Zo)/1 + a(2)*exp(-2)*(z-Zo)^2/2! + a(3)*exp(-3)*(z-Zo)^3/3! + ...
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REFERENCES
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D. Dominici, Nested derivatives: a simple method for computing series expansions of inverse functions, IJMMS 2003:58, 3699-3715.
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LINKS
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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Diego Dominici (dominicd(AT)newpaltz.edu), Jan 12 2004
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STATUS
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approved
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