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%I #21 Feb 27 2022 02:57:36
%S 1,1,1,0,-3,-9,-9,36,225,477,-819,-10944,-37179,16875,870507,4253796,
%T 2481921,-101978919,-680495175,-1060229088,16378166061,145672249311,
%U 368320357791,-3415036002300,-40270115077983,-141926533828299,882584266861701,13970371667206176
%N Expansion of e.g.f. exp(x - x^3/6).
%F a(n) = n! * Sum_{k=0..floor(n/3)} (-1/6)^k * binomial(n-2*k,k)/(n-2*k)!.
%F a(n) = a(n-1) - binomial(n-1,2) * a(n-3) for n > 2.
%t m = 27; Range[0, m]! * CoefficientList[Series[Exp[x - x^3/6], {x, 0, m}], x] (* _Amiram Eldar_, Feb 26 2022 *)
%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x-x^3/6)))
%o (PARI) a(n) = n!*sum(k=0, n\3, (-1/3!)^k*binomial(n-2*k, k)/(n-2*k)!);
%o (PARI) a(n) = if(n<3, 1, a(n-1)-binomial(n-1, 2)*a(n-3));
%Y Cf. A351930, A351931.
%Y Cf. A190865, A246607.
%K sign
%O 0,5
%A _Seiichi Manyama_, Feb 26 2022
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