OFFSET
0,3
COMMENTS
Here sigma(n,k) is the sum of the k-th powers of the divisors of n.
FORMULA
G.f.: exp( Sum_{n>=1} Sum_{k>=1} sigma(n,k) * x^(n*k)/n ).
Logarithmic derivative yields A198302.
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 5*x^3 + 12*x^4 + 18*x^5 + 42*x^6 + 62*x^7 +...
where the logarithm begins:
log(A(x)) = x + 5*x^2/2 + 7*x^3/3 + 21*x^4/4 + 11*x^5/5 + 65*x^6/6 + 15*x^7/7 + 133*x^8/8 + 106*x^9/9 +...+ A198302(n)*x^n/n +...
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, sumdiv(m, d, d*sigma(m/d, d))*x^m/m)+x*O(x^n)), n)}
(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, sum(k=1, n\m, sigma(m, k)*x^(m*k)/m)+x*O(x^n))), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 27 2012
STATUS
approved