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%I #14 Apr 18 2023 12:07:40
%S 1,1,1,1,1,-4,-35,-146,-447,-1133,10081,162625,1188001,6073354,
%T 24692669,-340585244,-8007557375,-83565282891,-598436312543,
%U -3348919070207,62583951520321,1933207863670000,26224985071994941,241528060568764586,1721188205642283841
%N a(n) = n! * Sum_{k=0..floor(n/5)} (-n/120)^k /(k! * (n-5*k)!).
%H Winston de Greef, <a href="/A362346/b362346.txt">Table of n, a(n) for n = 0..483</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F a(n) = n! * [x^n] exp(x - n*x^5/120).
%F E.g.f.: exp( ( 24*LambertW(x^5/24) )^(1/5) ) / (1 + LambertW(x^5/24)).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((24*lambertw(x^5/24))^(1/5))/(1+lambertw(x^5/24))))
%Y Cf. A362303, A362345.
%Y Cf. A351931.
%K sign
%O 0,6
%A _Seiichi Manyama_, Apr 16 2023