%I A156171
%S A156171 1,1,3,11,53,357,3521,51665,1122135,35638903,1639453459,108526044099,
%T A156171 10298220348807,1396920580458279,270394562069007327,
%U A156171 74574294532698008703,29276455806256470979269
%N A156171 G.f.: A(x) = exp( Sum_{n>=1} [x/(1 - 2^n*x)]^n/n ), a power series in 
               x with integer coefficients.
%e A156171 G.f.: A(x) = 1 + x + 3*x^2 + 11*x^3 + 53*x^4 + 357*x^5 + 3521*x^6 +...
%e A156171 log(A(x)) = x + 5*x^2/2 + 25*x^3/3 + 161*x^4/4 + 1441*x^5/5 + 18305*x^6/
               6 +...
%e A156171 Log series:
%e A156171 log(A(x)) = Sum_{n>=1} (x + 2^n*x^2 + 4^n*x^3 +...+ 2^(n(k-1))*x^k +...)^n/
               n.
%o A156171 (PARI) {a(n)=polcoeff(exp(sum(m=1,n,x^m/(1-2^m*x+x*O(x^n))^m/m)),n)}
%Y A156171 Cf. A156170, A155200, A156100.
%Y A156171 Sequence in context: A000255 A121580 A081367 this_sequence A129093 A057325 
               A054700
%Y A156171 Adjacent sequences: A156168 A156169 A156170 this_sequence A156172 A156173 
               A156174
%K A156171 nonn
%O A156171 0,3
%A A156171 Paul D. Hanna (pauldhanna(AT)juno.com), Feb 05 2009