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Expansion of e.g.f. exp(-2*x) / (1 + 2*log(1 - x)).
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%I #7 Dec 20 2023 12:37:13

%S 1,0,6,32,356,4456,68096,1211136,24625408,563266240,14315378880,

%T 400206928128,12205482237824,403262088466688,14348434923733504,

%U 546996936260529152,22243031618999642112,961019064912965103616,43963636798214215278592

%N Expansion of e.g.f. exp(-2*x) / (1 + 2*log(1 - x)).

%F a(n) = (-2)^n + 2 * Sum_{k=1..n} (k-1)! * binomial(n,k) * a(n-k).

%o (PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=(-2)^i+2*sum(j=1, i, (j-1)!*binomial(i, j)*v[i-j+1])); v;

%Y Cf. A088500, A343707, A368285, A368286.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Dec 19 2023