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%I #14 Apr 16 2023 11:28:10
%S 1,1,1,1,1,121,865,3529,10753,27217,7318081,96720625,689990401,
%T 3508289929,14239793569,5933573525881,114415115802625,
%U 1165402803391009,8298505279241857,46355961619888993,26167218073714552321,663290722580370585625
%N a(n) = n! * Sum_{k=0..floor(n/5)} (n/5)^k / (k! * (n-5*k)!).
%H Winston de Greef, <a href="/A362319/b362319.txt">Table of n, a(n) for n = 0..434</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^5/5).
%F E.g.f.: exp( ( -LambertW(-x^5) )^(1/5) ) / (1 + LambertW(-x^5)).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((-lambertw(-x^5))^(1/5))/(1+lambertw(-x^5))))
%Y Cf. A277614, A362300, A362314.
%K nonn
%O 0,6
%A _Seiichi Manyama_, Apr 16 2023