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A179467 G.f. satisfies: A(x) = exp( Sum_{n>=1} sigma(n)*A(x^n)*x^n/n ). 3

%I

%S 1,1,3,7,19,47,131,351,992,2808,8131,23723,70192,209209,629165,

%T 1904391,5801109,17764063,54663309,168925259,524064687,1631511342,

%U 5095440198,15960070908,50124189982,157806721089,497953049736,1574573746276

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

%F G.f.: Sum_{n>=0} a(n)*x^n = Product_{n>=1} P(x^n)^a(n-1) where P(x) = Product_{k>=1} 1/(1-x^k) is the partition function.

%e G.f.: A(x) = 1 + x + 3*x^2 + 7*x^3 + 19*x^4 + 47*x^5 + 131*x^6 +...

%e log(A(x)) = A(x)*x + 3*A(x^2)*x^2/2 + 4*A(x^3)*x^3/3 + 7*A(x^4)*x^4/4 +...

%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=exp(sum(m=1,n,subst(A,x,x^m+x*O(x^n))*sigma(m)*x^m/m)));polcoeff(A,n)}

%o (PARI) {a(n)=if(n<0,0,if(n==0,1,polcoeff(1/prod(m=1,n,prod(k=1,n\m+1,1-x^(k*m)+x*O(x^n))^a(m-1)),n)))}

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jul 15 2010

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Last modified October 25 16:58 EDT 2021. Contains 348255 sequences. (Running on oeis4.)