A061302 a(n) = n! * [x^n] W(-x)*(W(-x) + 2)/(W(-x) + 1), where W denotes Lambert's W function.

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.

Links

Table of n, a(n) for n=0..17.

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

Adjacent sequences: A061299 A061300 A061301 * A061303 A061304 A061305

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