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Expansion of e.g.f. exp(-x^3/6)/(1-x).
0

%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