A355084 E.g.f. A(x) satisfies A(x) = 1 + log(1+x) * A(2*x).
1, 1, 3, 32, 962, 74604, 14102416, 6268777248, 6394217598800, 14703540690658848, 75208658403123879744, 846736815151560907880448, 20804324374762392749905814784, 1107653447201119751335031683041792, 127026805293926861783650032004892737536
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)^(j-1)*2^(i-j)*(j-1)!*binomial(i, j)*v[i-j+1])); v;
Formula
a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k-1) * 2^(n-k) * (k-1)! * binomial(n,k) * a(n-k).