A375414 Expansion of e.g.f. exp(-x^3 * (1 - x)) / (1 - x).
1, 1, 2, 0, 24, 120, 1080, 2520, 40320, 302400, 4838400, 33264000, 498960000, 5448643200, 98075577600, 1242290649600, 21620216217600, 337903056691200, 6624678348288000, 119786633597030400, 2466692313845760000, 50371208660957184000, 1133144384491671552000
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x^3*(1-x))/(1-x))) -
PARI
a(n) = (-1)^n*n!*sum(k=0, n\3, binomial(k-1, n-3*k)/k!);
Formula
a(n) = (-1)^n * n! * Sum_{k=0..floor(n/3)} binomial(k-1,n-3*k)/k!.