A227831 - OEIS

%I #33 Jan 08 2021 14:26:39

%S 0,1,-1,3,-8,125,-54,16807,-16384,531441,-156250,2357947691,-2985984,

%T 1792160394037,-7909306972,320361328125,-35184372088832,

%U 2862423051509815793,-5083731656658,5480386857784802185939,-32000000000000000,41209797661291758429,-244636361793658185164

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

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

%D R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, 2nd ed., Eq. (5.66).

%D M. Kauers and P. Paule, The Concrete Tetrahedron, Springer 2011, p. 34.

%H Alois P. Heinz, <a href="/A227831/b227831.txt">Table of n, a(n) for n = 0..300</a>

%H R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, <a href="https://cs.uwaterloo.ca/research/tr/1993/03/W.pdf">On the Lambert W Function</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lambert_W_function">Lambert W function</a>

%F Numerators of series reversion of x/(Sum_{n=0..infinity} ((-x)^n)/n!). - _Mats Granvik_, Nov 24 2013

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

%p series(LambertW(x),x,30); # _N. J. A. Sloane_, Jan 08 2021

%t Numerator[CoefficientList[Series[LambertW[x], {x, 0, 22}], x]] (* _Mats Granvik_, Nov 24 2013 *)

%t Numerator[CoefficientList[InverseSeries[Series[x/Sum[((-x)^n)/Factorial[n], {n, 0, 22}], {x, 0, 22}]], x]] (* _Mats Granvik_, Nov 24 2013 *)

%Y Cf. A095996. See also A036504/A036503.

%K sign,frac

%O 0,4

%A _N. J. A. Sloane_, Aug 01 2013