A355235 E.g.f. A(x) satisfies A'(x) = 1 - log(1-x) * A(2*x)/2.

0, 1, 0, 2, 3, 40, 230, 4664, 69160, 2692320, 92337072, 7377183360, 561596031744, 94107667481472, 15571512343805184, 5506994273113257984, 1955013641428681233408, 1459378050438033715961856, 1101502067162420292961916928

Offset: 0

Author

Seiichi Manyama, Jun 25 2022

Keywords

• nonn

Crossrefs

Cf. A355230.

Programs

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);

Formula

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).