OFFSET
0,4
COMMENTS
The denominators are 1, 1, 1, 2, 3, 24, 5, 720, 315, 4480, 567, 3628800, 1925, ..., which is A095996 prefixed by 1.
REFERENCES
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.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..300
R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, On the Lambert W Function
Eric Weisstein's World of Mathematics, Lambert W-Function
Wikipedia, Lambert W function
FORMULA
Numerators of series reversion of x/(Sum_{n=0..infinity} ((-x)^n)/n!). - Mats Granvik, Nov 24 2013
EXAMPLE
0, 1, -1, 3/2, -8/3, 125/24, -54/5, 16807/720, -16384/315, 531441/4480, -156250/567, 2357947691/3628800, -2985984/1925, ...
MAPLE
series(LambertW(x), x, 30); # N. J. A. Sloane, Jan 08 2021
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Aug 01 2013
STATUS
approved