%I #7 Dec 19 2023 09:16:48
%S 1,-1,4,1,60,393,4498,54689,773384,12268369,216328614,4195769433,
%T 88776964444,2034936319817,50232646818890,1328570248040497,
%U 37481046375146640,1123486426007081505,35657224567565828302,1194561018775753556777,42125545306641497600036
%N Expansion of e.g.f. exp(-2*x) / (1 - x*exp(x)).
%F a(n) = n! * Sum_{k=0..n} (n-k-2)^k / k!.
%o (PARI) a(n) = n!*sum(k=0, n, (n-k-2)^k/k!);
%Y Cf. A006153, A072597, A092148, A368265.
%K sign,easy
%O 0,3
%A _Seiichi Manyama_, Dec 19 2023