OFFSET
0,2
COMMENTS
Here sigma(n) = A000203(n) is the sum of divisors of n. Compare g.f. to the formula for Jacobi theta_4(x) given by:
. theta_4(x) = exp( Sum_{n>=1} (sigma(n)-sigma(2n))*x^n/n )
where theta_4(x) = 1 + Sum_{n>=1} 2*(-x)^(n^2).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..400 from Paul D. Hanna)
EXAMPLE
G.f.: A(x) = 1 + 4*x + 16*x^2 + 64*x^3 + 208*x^4 + 656*x^5 +...
log(A(x)) = 4*x + 16*x^2/2 + 64*x^3/3 +...+ A054785(n)^2*x^n/n +...
MATHEMATICA
nmax = 30; CoefficientList[Series[Exp[Sum[(DivisorSigma[1, 2*k] - DivisorSigma[1, k])^2 * x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 26 2019 *)
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n, (sigma(2*m)-sigma(m))^2*x^m/m)+x*O(x^n)), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 30 2010
STATUS
approved