%I #6 Feb 27 2024 09:48:09
%S 1,1,2,5,20,100,610,4270,34160,307160,3071600,33787600,405466600,
%T 5271065800,73794921200,1106922416600,17710758665600,301082897315200,
%U 5419492342264000,102970354503016000,2059407090060320000,43247548855054544000,951446074811199968000
%N Expansion of e.g.f. exp(-x^3/6)/(1-x).
%F a(n) = n! * Sum_{k=0..floor(n/3)} (-1)^k/(6^k * k!).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x^3/6)/(1-x)))
%o (PARI) a(n) = n!*sum(k=0, n\3, (-1)^k/(6^k*k!));
%Y Cf. A000166, A000266.
%K nonn,easy
%O 0,3
%A _Seiichi Manyama_, Feb 27 2024