A355123 E.g.f. A(x) satisfies A(x) = 1 + (1 - exp(-x)) * A(2 * (1 - exp(-x))).
1, 1, 3, 25, 611, 41721, 7326115, 3120454233, 3105527125475, 7041597540281017, 35733375744777784867, 400526056950063657595929, 9816824637930442994222501475, 521959475771315485798501882623609, 59814953381855591853355367174623538851
Offset: 0
Keywords
Programs
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PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (-1)^(i-j)*j*2^(j-1)*stirling(i, j, 2)*v[j])); v;
Formula
E.g.f. A(x) satisfies: A(-log(1-x)) = 1 + x*A(2*x).
a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(n-k) * k * 2^(k-1) * Stirling2(n,k) * a(k-1).