OFFSET
0,3
COMMENTS
Here sigma(n,k) equals the sum of the k-th powers of the divisors of n.
FORMULA
G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=1..n} binomial(n,k) * sigma(n,k) ).
EXAMPLE
G.f.: A(x) = 1 + x + 6*x^2 + 29*x^3 + 221*x^4 + 1897*x^5 + 23502*x^6 +...
where the g.f. equals the product:
A(x) = (1-x)/(1-2*x) * ((1-x^2)/(1-3^2*x^2))^(1/2) * ((1-x^3)/(1-4^3*x^3))^(1/3) * ((1-x^4)/(1-5^4*x^4))^(1/4) * ((1-x^5)/(1-6^5*x^5))^(1/5) *...
The logarithm equals the l.g.f. of A205812:
log(A(x)) = x + 11*x^2/2 + 70*x^3/3 + 719*x^4/4 + 7806*x^5/5 + 122534*x^6/6 +...
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, x^m/m*sum(k=1, m, binomial(m, k)*sigma(m, k))+x*O(x^n))), n)}
(PARI) {a(n)=polcoeff(prod(k=1, n, ((1-x^k)/(1-(k+1)^k*x^k +x*O(x^n)))^(1/k)), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 01 2012
STATUS
approved