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Expansion of e.g.f. exp(x - x^3/3).
2

%I #18 Apr 16 2023 09:51:26

%S 1,1,1,-1,-7,-19,1,211,1009,953,-14239,-105049,-209879,1669669,

%T 18057313,56255291,-294375199,-4628130319,-19929569471,70149241423,

%U 1652969810521,9226206209501,-20236475188159,-783908527648861,-5452368869656367

%N Expansion of e.g.f. exp(x - x^3/3).

%H Seiichi Manyama, <a href="/A362309/b362309.txt">Table of n, a(n) for n = 0..632</a>

%F a(n) = a(n-1) - 2 * binomial(n-1,2) * a(n-3) for n > 2.

%F a(n) = n! * Sum_{k=0..floor(n/3)} (-1/3)^k / (k! * (n-3*k)!).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-x^3/3)))

%Y Column k=2 of A362302.

%Y Cf. A001470, A246607.

%K sign,easy

%O 0,5

%A _Seiichi Manyama_, Apr 15 2023