A355086 E.g.f. A(x) satisfies A(x) = 1 - log(1-x) * A(2*x).
1, 1, 5, 68, 2318, 191364, 37322176, 16851654336, 17323677619888, 39991811695203552, 204958165376127918144, 2309776412016044230960128, 56778926016923229432156258048, 3023733345610004146919028796718592
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, 2^(i-j)*(j-1)!*binomial(i, j)*v[i-j+1])); v;
Formula
a(0) = 1; a(n) = Sum_{k=1..n} 2^(n-k) * (k-1)! * binomial(n,k) * a(n-k).