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A159595 G.f.: A(x) = exp( Sum_{n>=1} [ Sum_{k>=1} sigma(k,n)*x^k ]^n/n ).

%I A159595 #6 Nov 26 2022 21:15:35
%S A159595 1,1,4,13,56,286,2008,19749,280842,5762129,168873970,7023348917,
%T A159595 412682000624,34188301513404,3992802803844526,656649238572375132,
%U A159595 152278229304524217542,49749953321847000835094
%N A159595 G.f.: A(x) = exp( Sum_{n>=1} [ Sum_{k>=1} sigma(k,n)*x^k ]^n/n ).
%C A159595 Define sigma(k,n) = Sum_{d|k} d^n.
%e A159595 G.f.: A(x) = 1 + x + 4*x^2 + 13*x^3 + 56*x^4 + 286*x^5 + 2008*x^6 +...
%e A159595 log(A(x)) = Sum_{n>=1} [x + sigma(2,n)*x^2 + sigma(3,n)*x^3 +...]^n/n.
%o A159595 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=exp(sum(m=1,n,sum(k=1,n,sigma(k,m)*x^k+x*O(x^n))^m/m)));polcoeff(A,n)}
%o A159595 for(n=0,20,print1(a(n),", "))
%Y A159595 Cf. A159604.
%K A159595 nonn
%O A159595 0,3
%A A159595 _Paul D. Hanna_, May 05 2009