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A227831
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Numerators of coefficients in Taylor series for LambertW(x).
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2
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0, 1, -1, 3, -8, 125, -54, 16807, -16384, 531441, -156250, 2357947691, -2985984, 1792160394037, -7909306972, 320361328125, -35184372088832, 2862423051509815793, -5083731656658, 5480386857784802185939, -32000000000000000, 41209797661291758429, -244636361793658185164
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OFFSET
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0,4
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COMMENTS
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The denominators are 1, 1, 1, 2, 3, 24, 5, 720, 315, 4480, 567, 3628800, 1925, ..., which is A095996 prefixed by 1.
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REFERENCES
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R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, 2nd ed., Eq. (5.66).
M. Kauers and P. Paule, The Concrete Tetrahedron, Springer 2011, p. 34.
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LINKS
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FORMULA
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Numerators of series reversion of x/(Sum_{n=0..infinity} ((-x)^n)/n!). - Mats Granvik, Nov 24 2013
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EXAMPLE
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0, 1, -1, 3/2, -8/3, 125/24, -54/5, 16807/720, -16384/315, 531441/4480, -156250/567, 2357947691/3628800, -2985984/1925, ...
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MAPLE
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MATHEMATICA
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Numerator[CoefficientList[Series[LambertW[x], {x, 0, 22}], x]] (* Mats Granvik, Nov 24 2013 *)
Numerator[CoefficientList[InverseSeries[Series[x/Sum[((-x)^n)/Factorial[n], {n, 0, 22}], {x, 0, 22}]], x]] (* Mats Granvik, Nov 24 2013 *)
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CROSSREFS
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KEYWORD
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sign,frac
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AUTHOR
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STATUS
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approved
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