A179467 G.f. satisfies: A(x) = exp( Sum_{n>=1} sigma(n)*A(x^n)*x^n/n ).
1, 1, 3, 7, 19, 47, 131, 351, 992, 2808, 8131, 23723, 70192, 209209, 629165, 1904391, 5801109, 17764063, 54663309, 168925259, 524064687, 1631511342, 5095440198, 15960070908, 50124189982, 157806721089, 497953049736, 1574573746276
Offset: 0
Keywords
Examples
G.f.: A(x) = 1 + x + 3*x^2 + 7*x^3 + 19*x^4 + 47*x^5 + 131*x^6 +... 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 +...
Programs
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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)} -
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)))}
Formula
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.