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A102743
Expansion of e.g.f. LambertW(-x)/(x*(x-1)).
3
1, 2, 7, 37, 273, 2661, 32773, 491555, 8715409, 178438681, 4142334501, 107483043735, 3081956918857, 96759352320437, 3300826000845493, 121569984050610331, 4807542796319581089, 203167758634027130289
OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
a(n) = n!*Sum_{k=1..n+1} k^(k-1)/k!. - Vladeta Jovovic, Oct 17 2007
a(n) ~ exp(2)/(exp(1)-1) * n^(n-1). - Vaclav Kotesovec, Nov 27 2012
E.g.f.: W(0)/(2-2*x) , where W(k) = 1 + 1/( 1 - x*(k+2)^k/( x*(k+2)^k + (k+1)^k/W(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Aug 19 2013
From Seiichi Manyama, May 01 2023: (Start)
E.g.f.: exp(-LambertW(-x))/(1-x).
a(0) = 1; a(n) = n*a(n-1) + (n+1)^(n-1). (End)
MATHEMATICA
CoefficientList[Series[LambertW[-x]/(x*(x-1)), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Nov 27 2012 *)
PROG
(PARI) my(x='x+O('x^50)); Vec(serlaplace(lambertw(-x)/(x*(x-1)))) \\ G. C. Greubel, Nov 08 2017
CROSSREFS
Cf. A277506.
Sequence in context: A001028 A116481 A367494 * A195068 A342412 A196916
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Feb 08 2005
STATUS
approved