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%I #16 Apr 17 2023 09:26:39
%S 1,1,1,1,1,601,4321,17641,53761,136081,181742401,2415576241,
%T 17245198081,87699217321,355981385761,736792782125401,
%U 14287010845685761,145634558983324321,1037210264169367681,5794253172081059041,16246379099801447769601
%N a(n) = n! * Sum_{k=0..floor(n/5)} n^k / (k! * (n-5*k)!).
%H Seiichi Manyama, <a href="/A362323/b362323.txt">Table of n, a(n) for n = 0..414</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).
%F E.g.f.: exp( ( -LambertW(-5*x^5)/5 )^(1/5) ) / (1 + LambertW(-5*x^5)).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((-lambertw(-5*x^5)/5)^(1/5))/(1+lambertw(-5*x^5))))
%Y Cf. A362301, A362321.
%Y Cf. A190877, A362319.
%K nonn
%O 0,6
%A _Seiichi Manyama_, Apr 16 2023
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