A352376 - OEIS

%I #24 Oct 11 2024 12:35:46

%S 1,-2,1,6,-2,-58,-91,732,4365,-1468,-140682,-685886,1791101,43923266,

%T 216543097,-939472974,-22047365454,-127801626362,541608607233,

%U 16524264652568,124850392700061,-279906371211584,-16968403342944782,-176737444660619046

%N Expansion of e.g.f. exp(1 - (1 + x) * exp(x)).

%H Seiichi Manyama, <a href="/A352376/b352376.txt">Table of n, a(n) for n = 0..554</a>

%F a(0) = 1; a(n) = -Sum_{k=1..n} (k+1) * binomial(n-1,k-1) * a(n-k).

%t With[{nn=30},CoefficientList[Series[Exp[1-(1+x)Exp[x]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Oct 11 2024 *)

%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(1-(1+x)*exp(x))))

%o (PARI) a(n) = if(n==0, 1, -sum(k=1, n, (k+1)*binomial(n-1, k-1)*a(n-k)));

%Y Cf. A209801, A345652.

%K sign

%O 0,2

%A _Seiichi Manyama_, Mar 15 2022