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%I #15 Feb 25 2022 12:11:08
%S 1,1,1,1,-23,-119,-359,-839,18481,178417,902161,3318481,-69866279,
%T -1011908039,-7204341143,-36194591159,726745175521,14326789219681,
%U 131901636673441,840736509931297,-16060449291985079,-408041402342457239,-4618341644958693959,-35691963052019431079
%N Expansion of e.g.f. exp(x * (1 - x^3)).
%F a(n) = n! * Sum_{k=0..floor(n/4)} (-1)^k * binomial(n-3*k,k)/(n-3*k)!.
%F a(n) = a(n-1) - 4! * binomial(n-1,3) * a(n-4) for n > 3.
%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x*(1-x^3))))
%o (PARI) a(n) = n!*sum(k=0, n\4, (-1)^k*binomial(n-3*k, k)/(n-3*k)!);
%o (PARI) a(n) = if(n<4, 1, a(n-1)-4!*binomial(n-1, 3)*a(n-4));
%Y Cf. A293604, A246607, A351906.
%Y Cf. A190875, A293493.
%K sign
%O 0,5
%A _Seiichi Manyama_, Feb 25 2022
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