OFFSET
0,3
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.
EXAMPLE
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 +...
PROG
(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)))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 15 2010
STATUS
approved