%I A158107
%S A158107 1,1,2,7,44,272,3053,25670,368728,4867442,86339238,1071067999,
%T A158107 28751805809,417861397848,9791134239124,235308903842756,
%U A158107 7238087265282704,133575559401222741,5068916834663575735
%N A158107 G.f.: A(x) = exp( Sum_{n>=1} sigma(n)*L(n)*x^n/n ) where Sum_{n>=1} L(n)*x^n/
               n = log(1+x*A(x)).
%e A158107 G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 44*x^4 + 272*x^5 + 3053*x^6 +...
%e A158107 log(1+x*A(x)) = x + x^2/2 + 4*x^3/3 + 21*x^4/4 + 186*x^5/5 + 1366*x^6/
               6 +...
%e A158107 log(A(x)) = x + 3*x^2/2 + 16*x^3/3 + 147*x^4/4 + 1116*x^5/5 + 16392*x^6/
               6 +...
%e A158107 log(A(x)) = x + 3*1*x^2/2 + 4*4*x^3/3 + 7*21*x^4/4 + 6*186*x^5/5 + 12*1366*x^6/
               6 +...
%o A158107 (PARI) {a(n)=local(A=1+x);if(n==0,1,for(i=1,n,A=exp(sum(m=1,n,sigma(m)*x^m*polcoeff(log(1+x*A+x*O(x^m)),
               m))+x*O(x^n)));polcoeff(A,n))}
%Y A158107 Cf. A158108.
%Y A158107 Sequence in context: A011835 A103084 A041507 this_sequence A145073 A111561 
               A000155
%Y A158107 Adjacent sequences: A158104 A158105 A158106 this_sequence A158108 A158109 
               A158110
%K A158107 nonn
%O A158107 0,3
%A A158107 Paul D. Hanna (pauldhanna(AT)juno.com), Mar 28 2009