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A358185
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Coefficients of x^n/n! in the expansion of (1 - x)*log(1 - x).
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0
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0, -1, 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000, 51090942171709440000, 1124000727777607680000, 25852016738884976640000
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OFFSET
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0,5
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COMMENTS
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The negated sequence gives the compositional inverse of 1 - exp(W(-x)) with the principal branch of Lambert's W function.
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LINKS
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FORMULA
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E.g.f.: (1 - x) * log(1 - x).
a(0) = 0, a(1) = -1, a(n) = (n-2)! = A000142(n-2), for n >= 2.
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MATHEMATICA
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With[{m = 25}, Range[0, m]! * CoefficientList[Series[(1-x) * Log[1-x], {x, 0, m}], x]] (* Amiram Eldar, Nov 14 2022 *)
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PROG
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(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x)*log(1-x)), -N) \\ Michel Marcus, Sep 16 2023
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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