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%I #6 Nov 26 2022 21:15:18
%S 1,1,6,43,856,10744,608375,14284223,551011548,19119025101,
%T 874788949035,37896009869060,20683158266928833,1799893777863733707,
%U 93147805938921355288,3757831283217050847983,180287028377782585130749
%N G.f.: A(x) = exp( Sum_{n>=1} [ Sum_{k>=1} sigma(n,k)*x^k ]^n/n ).
%C Define sigma(n,k) = Sum_{d|n} d^k.
%H Paul D. Hanna, <a href="/A159604/b159604.txt">Table of n, a(n) for n = 0..510</a>
%e G.f.: A(x) = 1 + x + 6*x^2 + 43*x^3 + 856*x^4 + 10744*x^5 +...
%e log(A(x)) = Sum_{n>=1} [sigma(n)*x + sigma(n,2)*x^2 + sigma(n,3)*x^3 +...]^n/n.
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=exp(sum(m=1,n,sum(k=1,n,sigma(m,k)*x^k+x*O(x^n))^m/m)));polcoeff(A,n)}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. variants: A159595, A156217.
%K nonn
%O 0,3
%A _Paul D. Hanna_, May 16 2009
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