OFFSET
0,2
REFERENCES
Stephan Wolfram, The Mathematica Book, 4th Edition, Cambridge University Press, section 3.2.10 'Special Functions', page 772, 1999.
FORMULA
a(n) = (n+1)*n^(n-1) with a(0) = 0.
EXAMPLE
2*x + 6*x^2 +36*x^3 + 320*x^4 + 3750*x^5 + 54432*x^6 + 941192*x^7 + ...
MAPLE
W := LambertW: egf := -W(-x)*(W(-x) + 2)/(W(-x) + 1):
ser := series(egf, x, 20): seq(n!*coeff(ser, x, n), n = 0..17); # Peter Luschny, Feb 10 2023
MATHEMATICA
Range[18]!CoefficientList[ Series[ -ProductLog[ -x], {x, 0, 17}], x] (* Robert G. Wilson v, Mar 23 2005 *)
a[ n_] := If[ n < 0, 0, (n + 1)! SeriesCoefficient[ -ProductLog[-x], {x, 0, n}]] (* Michael Somos, Jun 07 2012 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gero Burghardt (gerogoestohollywood(AT)yahoo.de), Jun 05 2001
EXTENSIONS
Corrected and extended by Jason Earls, Jun 09 2001
Name made consistent with offset by Peter Luschny, Feb 10 2023
STATUS
approved