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%I #28 Feb 25 2022 11:55:54
%S 1,1,1,-5,-23,-59,241,2311,9745,-30743,-529919,-3161069,6984121,
%T 216832045,1696212337,-2117117729,-138721306079,-1359994188719,
%U 367573878145,127713732858667,1523067770484361,1104033549399061,-159815269852521359,-2270787199743845705,-3946710127731620303
%N Expansion of e.g.f. exp(x - x^3).
%H Vincenzo Librandi, <a href="/A246607/b246607.txt">Table of n, a(n) for n = 0..200</a>
%F From _Seiichi Manyama_, Feb 25 2022: (Start)
%F a(n) = n! * Sum_{k=0..floor(n/3)} (-1)^k * binomial(n-2*k,k)/(n-2*k)!.
%F a(n) = a(n-1) - 3! * binomial(n-1,2) * a(n-3) for n > 2. (End)
%t Range[0, 24]! CoefficientList[Series[Exp[x - x^3], {x, 0, 24}], x] (* _Robert G. Wilson v_, Aug 31 2014, with correction from _Vincenzo Librandi_ *)
%o (PARI) default(seriesprecision, 30); serlaplace(exp(x-x^3)) \\ _Michel Marcus_, Aug 31 2014
%o (PARI) a(n) = n!*sum(k=0, n\3, (-1)^k*binomial(n-2*k, k)/(n-2*k)!); \\ _Seiichi Manyama_, Feb 25 2022
%o (PARI) a(n) = if(n<3, 1, a(n-1)-3!*binomial(n-1, 2)*a(n-3)); \\ _Seiichi Manyama_, Feb 25 2022
%Y Cf. A118395, A293604.
%K sign
%O 0,4
%A _Robert G. Wilson v_, Aug 31 2014