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

Author

N. J. A. Sloane, Aug 01 2013

Keywords

• sign
• frac

Comments

The denominators are 1, 1, 1, 2, 3, 24, 5, 720, 315, 4480, 567, 3628800, 1925, ..., which is A095996 prefixed by 1.

Examples

			0, 1, -1, 3/2, -8/3, 125/24, -54/5, 16807/720, -16384/315, 531441/4480, -156250/567, 2357947691/3628800, -2985984/1925, ...
		

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

Crossrefs

Cf. A095996. See also A036504/A036503.

Programs

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 *)

Formula

Numerators of series reversion of x/(Sum_{n=0..infinity} ((-x)^n)/n!). - Mats Granvik, Nov 24 2013