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A061302
a(n) = n! * [x^n] W(-x)*(W(-x) + 2)/(W(-x) + 1), where W denotes Lambert's W function.
1
0, 2, 6, 36, 320, 3750, 54432, 941192, 18874368, 430467210, 11000000000, 311249095212, 9659108818944, 326173191714734, 11905721598812160, 467086816406250000, 19599665578316398592, 875901453762003632658
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
Cf. A061250.
Essentially the same as A055541.
Sequence in context: A277393 A182037 A306066 * A055541 A275551 A321085
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