%I #25 Apr 18 2023 08:28:42
%S 1,1,1,1,1,6,37,148,449,1135,15121,172789,1207009,6106816,24748725,
%T 510855346,8524169473,84981641837,602009065729,3357322881625,
%U 93871272204481,2059974308136466,26683062726210661,243032907824598816,1725747644222610625
%N a(n) = n! * Sum_{k=0..floor(n/5)} (n/120)^k /(k! * (n-5*k)!).
%H Seiichi Manyama, <a href="/A362336/b362336.txt">Table of n, a(n) for n = 0..484</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. A362173, A362317.
%Y Cf. A275423, A362319, A362323.
%K nonn
%O 0,6
%A _Seiichi Manyama_, Apr 16 2023
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