OFFSET
0,3
COMMENTS
If prefixed by an additional 1, numerators of coefficients of expansion of exp(W(x)). - N. J. A. Sloane, Jan 08 2021
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..388
Wikipedia, Lambert W function
FORMULA
a(n) = (-1)^n*numerator(g(n)) where g(n) = n^n/n!.
a(n) = (-1)^n*denominator(h(n)) where h(n) = Sum_{k=0..n-1}(n!*n^k)/(k!*n^n).
EXAMPLE
Coefficients of expansion of exp(W(x)) are 1, 1, -1/2, 2/3, -9/8, 32/15, -625/144, 324/35, -117649/5760, 131072/2835, -4782969/44800, ... - N. J. A. Sloane, Jan 08 2021
MAPLE
seq(numer((-1)^n*n^n/n!), n = 0..21);
MATHEMATICA
CoefficientList[Series[1/ProductLog[x] - 1/x, {x, 0, 21}], x] // Numerator
PROG
(PARI) vector(22, n, n--; (-1)^n*numerator(n^n/n!)) \\ Altug Alkan, Nov 09 2015
(Magma) [(-1)^n * Numerator(n^n/Factorial(n)): n in [0..50]]; // G. C. Greubel, Nov 14 2017
CROSSREFS
KEYWORD
sign,frac
AUTHOR
Peter Luschny, Nov 09 2015
STATUS
approved