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%I #18 Mar 29 2024 19:10:14
%S 1,-4,4,56,-104,-2464,1696,181184,462016,-17069824,-141580544,
%T 1593913856,33015560704,-47193585664,-6973651011584,-50207289585664,
%U 1214484253413376,25500259291480064,-72069247145590784,-8696105637665603584,-81680899029758541824
%N Expansion of e.g.f. exp(1 - (1+x)^4).
%F a(0) = 1; a(n) = -4 * (n-1)! * Sum_{k=1..min(4,n)} binomial(3,k-1) * a(n-k)/(n-k)!.
%F a(n) = Sum_{k=0..n} 4^k * Stirling1(n,k) * A000587(k).
%F D-finite with recurrence a(n) +4*a(n-1) +12*(n-1)*a(n-2) +12*(n-1)*(n-2)*a(n-3) +4*(n-1)*(n-2)*(n-3)*a(n-4)=0. - _R. J. Mathar_, Feb 02 2024
%t With[{nn=20},CoefficientList[Series[Exp[1-(1+x)^4],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Mar 29 2024 *)
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(1-(1+x)^4)))
%Y Column k=4 of A369738.
%Y Cf. A000587, A202824.
%K sign
%O 0,2
%A _Seiichi Manyama_, Jan 30 2024