A351929 Expansion of e.g.f. exp(x - x^3/6).
1, 1, 1, 0, -3, -9, -9, 36, 225, 477, -819, -10944, -37179, 16875, 870507, 4253796, 2481921, -101978919, -680495175, -1060229088, 16378166061, 145672249311, 368320357791, -3415036002300, -40270115077983, -141926533828299, 882584266861701, 13970371667206176
Offset: 0
Keywords
Programs
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Mathematica
m = 27; Range[0, m]! * CoefficientList[Series[Exp[x - x^3/6], {x, 0, m}], x] (* Amiram Eldar, Feb 26 2022 *) -
PARI
my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x-x^3/6))) -
PARI
a(n) = n!*sum(k=0, n\3, (-1/3!)^k*binomial(n-2*k, k)/(n-2*k)!);
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PARI
a(n) = if(n<3, 1, a(n-1)-binomial(n-1, 2)*a(n-3));
Formula
a(n) = n! * Sum_{k=0..floor(n/3)} (-1/6)^k * binomial(n-2*k,k)/(n-2*k)!.
a(n) = a(n-1) - binomial(n-1,2) * a(n-3) for n > 2.