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E.g.f. A(x) satisfies A'(x) = 1 - log(1-x) * A(2*x)/2.
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%I #14 Jun 25 2022 10:00:46

%S 0,1,0,2,3,40,230,4664,69160,2692320,92337072,7377183360,561596031744,

%T 94107667481472,15571512343805184,5506994273113257984,

%U 1955013641428681233408,1459378050438033715961856,1101502067162420292961916928

%N E.g.f. A(x) satisfies A'(x) = 1 - log(1-x) * A(2*x)/2.

%F a(0) = 0, a(1) = 1; a(n+1) = Sum_{k=1..n-1} 2^(n-k-1) * (k-1)! * binomial(n,k) * a(n-k).

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

%Y Cf. A355230.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Jun 25 2022