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%I #18 Feb 20 2018 09:00:25
%S 1,20,360,6860,143570,3321864,84756000,2372001720,72384192540,
%T 2394775746220,85443353291296,3271908306712500,133893717061821080,
%U 5832748749666611920,269542701201588099840,13172225935626444660144,678788199609330554538000,36790272488566573278647940
%N Expansion of e.g.f.: exp((-1)^k/k*LambertW(-x)^k)/(k-1)!, k=4.
%C a(n) = A243098(n,4)/6. - _Alois P. Heinz_, Aug 19 2014
%H Vincenzo Librandi, <a href="/A060918/b060918.txt">Table of n, a(n) for n = 4..200</a>
%F a(n) = (n-1)!/(k-1)!*Sum_{i=0..floor((n-k)/k)} 1/(i!*k^i)*n^(n-(i+1)*k)/(n-(i+1)*k)!, k=4.
%F a(n) ~ 1/6*exp(1/4)*n^(n-1). - _Vaclav Kotesovec_, Nov 27 2012
%t CoefficientList[Series[E^(1/4*LambertW[-x]^4)/6, {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Nov 27 2012 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(lambertw(-x)^4/4)/3! - 1/3!)) \\ _G. C. Greubel_, Feb 19 2018
%Y Cf. A057817, A060917, A243098.
%K easy,nonn
%O 4,2
%A _Vladeta Jovovic_, Apr 10 2001