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

%I #6 Nov 26 2022 21:15:35

%S 1,1,4,13,56,286,2008,19749,280842,5762129,168873970,7023348917,

%T 412682000624,34188301513404,3992802803844526,656649238572375132,

%U 152278229304524217542,49749953321847000835094

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

%C Define sigma(k,n) = Sum_{d|k} d^n.

%e G.f.: A(x) = 1 + x + 4*x^2 + 13*x^3 + 56*x^4 + 286*x^5 + 2008*x^6 +...

%e log(A(x)) = Sum_{n>=1} [x + sigma(2,n)*x^2 + sigma(3,n)*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(k,m)*x^k+x*O(x^n))^m/m)));polcoeff(A,n)}

%o for(n=0,20,print1(a(n),", "))

%Y Cf. A159604.

%K nonn

%O 0,3

%A _Paul D. Hanna_, May 05 2009

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