A227831 Numerators of coefficients in Taylor series for LambertW(x).

0, 1, -1, 3, -8, 125, -54, 16807, -16384, 531441, -156250, 2357947691, -2985984, 1792160394037, -7909306972, 320361328125, -35184372088832, 2862423051509815793, -5083731656658, 5480386857784802185939, -32000000000000000, 41209797661291758429, -244636361793658185164

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

Cf. A095996. See also A036504/A036503.

Sequence in context: A192629 A245458 A036504 * A132491 A083112 A053605

Adjacent sequences: A227828 A227829 A227830 * A227832 A227833 A227834

Keyword

sign,frac

Author

N. J. A. Sloane, Aug 01 2013

Status

approved