%I #23 Jul 30 2022 04:37:10
%S 1,-1,-1,-1,25,19,-209,-2269,2801,68615,371071,-2499641,-28306871,
%T -58645861,1964456495,15133179179,-37119981599,-1861550428529,
%U -9225044407169,110317002942095,2150185424201081,3953685082287779,-233260896605772881,-2920858244957587661,7649165533910291665
%N E.g.f.: exp(-(x + x^2 + x^3)).
%H Seiichi Manyama, <a href="/A334562/b334562.txt">Table of n, a(n) for n = 0..500</a>
%F a(0) = 1 and a(n) = - (n-1)! * Sum_{k=1..min(3,n)} k*a(n-k)/(n-k)!.
%F D-finite with recurrence a(n) + a(n-1) +2*(n-1)*a(n-2) +3*(n-1)*(n-2)*a(n-3)=0. - _R. J. Mathar_, May 07 2020
%t With[{nn=30},CoefficientList[Series[Exp[-(x+x^2+x^3)],{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Nov 26 2020 *)
%o (PARI) N=40; x='x+O('x^N); Vec(serlaplace(exp(-x-x^2-x^3)))
%Y Column 3 of A334561.
%Y Cf. A118589, A334569.
%K sign
%O 0,5
%A _Seiichi Manyama_, May 06 2020