A351931 - OEIS

%I #16 Feb 27 2022 02:57:13

%S 1,1,1,1,1,0,-5,-20,-55,-125,-125,925,7525,34750,124125,249250,

%T -1013375,-14708875,-97413875,-477236375,-1443329375,3466472500,

%U 91499089375,804081585000,5030009685625,20366827624375,-23484049500625,-1391395435656875,-15503027252406875

%N Expansion of e.g.f. exp(x - x^5/120).

%F a(n) = n! * Sum_{k=0..floor(n/5)} (-1/5!)^k * binomial(n-4*k,k)/(n-4*k)!.

%F a(n) = a(n-1) - binomial(n-1,4) * a(n-5) for n > 4.

%t m = 28; Range[0, m]! * CoefficientList[Series[Exp[x - x^5/5!], {x, 0, m}], x] (* _Amiram Eldar_, Feb 26 2022 *)

%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x-x^5/5!)))

%o (PARI) a(n) = n!*sum(k=0, n\5, (-1/5!)^k*binomial(n-4*k, k)/(n-4*k)!);

%o (PARI) a(n) = if(n<5, 1, a(n-1)-binomial(n-1, 4)*a(n-5));

%Y Cf. A351929, A351930.

%Y Cf. A275423, A351906.

%K sign

%O 0,7

%A _Seiichi Manyama_, Feb 26 2022