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A177398 O.g.f.: exp( Sum_{n>=1} (sigma(2n)-sigma(n))^2 * x^n/n ). 4
1, 4, 16, 64, 208, 656, 1984, 5632, 15520, 41476, 107312, 271232, 670464, 1622160, 3854208, 9003264, 20696640, 46895248, 104827472, 231353984, 504592448, 1088323584, 2322683072, 4908033280, 10273819136, 21313971876, 43843093488 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A027676 A249567 A348906 * A343200 A227312 A267729
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 30 2010
STATUS
approved

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Last modified July 14 13:51 EDT 2024. Contains 374318 sequences. (Running on oeis4.)