A351931 Expansion of e.g.f. exp(x - x^5/120).
1, 1, 1, 1, 1, 0, -5, -20, -55, -125, -125, 925, 7525, 34750, 124125, 249250, -1013375, -14708875, -97413875, -477236375, -1443329375, 3466472500, 91499089375, 804081585000, 5030009685625, 20366827624375, -23484049500625, -1391395435656875, -15503027252406875
Offset: 0
Keywords
Programs
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Mathematica
m = 28; Range[0, m]! * CoefficientList[Series[Exp[x - x^5/5!], {x, 0, m}], x] (* Amiram Eldar, Feb 26 2022 *) -
PARI
my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x-x^5/5!))) -
PARI
a(n) = n!*sum(k=0, n\5, (-1/5!)^k*binomial(n-4*k, k)/(n-4*k)!);
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PARI
a(n) = if(n<5, 1, a(n-1)-binomial(n-1, 4)*a(n-5));
Formula
a(n) = n! * Sum_{k=0..floor(n/5)} (-1/5!)^k * binomial(n-4*k,k)/(n-4*k)!.
a(n) = a(n-1) - binomial(n-1,4) * a(n-5) for n > 4.