A292908 - OEIS

%I #24 Jul 10 2022 09:41:10

%S 1,0,0,6,-24,60,240,-4830,39984,-180936,-605520,24616350,-318005160,

%T 2385790836,-86488584,-350543790870,6917020827360,-79778558317200,

%U 357117438258144,9237998478286134,-304182278908538040,5166739059890655660,-48968796671246843160

%N Expansion of e.g.f. exp(x^3 * exp(-x)).

%H Seiichi Manyama, <a href="/A292908/b292908.txt">Table of n, a(n) for n = 0..505</a>

%F a(n) = n! * Sum_{k=0..floor(n/3)} (-k)^(n-3*k)/(k! * (n-3*k)!). - _Seiichi Manyama_, Jul 10 2022

%o (PARI) x='x+O('x^66); Vec(serlaplace(exp(x^3*exp(-x))))

%o (PARI) a(n) = n!*sum(k=0, n\3, (-k)^(n-3*k)/(k!*(n-3*k)!)); \\ _Seiichi Manyama_, Jul 10 2022

%Y Column k=3 of A292973.

%Y Cf. A292889.

%K sign

%O 0,4

%A _Seiichi Manyama_, Sep 26 2017