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%I #12 Feb 16 2025 08:34:05
%S 1,1,1,2,5,11,51,246,897,7085,51221,260426,2938541,28279967,184234415,
%T 2714662406,32614422401,259026339161,4721237878537,67998862785970,
%U 637019875964341,13852253151455251,232584488748665131,2510358957337412182,63466995535914172225
%N a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)^(k-1) / (6^k * k! * (n-3*k)!).
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F E.g.f.: exp(x - LambertW(-x^3/6)) = -6 * LambertW(-x^3/6)/x^3 * exp(x).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-x^3/6))))
%Y Cf. A088957, A362524.
%Y Cf. A362351, A362523.
%K nonn,easy
%O 0,4
%A _Seiichi Manyama_, Apr 23 2023