OFFSET
1,2
FORMULA
E.g.f.: -log(theta_4(x)) / 2.
E.g.f.: (1/2) * Sum_{k>=1} log((1 + x^k) / (1 - x^k)).
E.g.f.: log(Product_{k>=1} ((1 + x^k) / (1 - x^k))^(1/2)).
E.g.f.: Sum_{k>=1} x^(2*k - 1) / ((2*k - 1) * (1 - x^(2*k - 1))).
exp(2 * Sum_{n>=1} a(n) * x^n / n!) = g.f. of A015128.
a(n) = (n - 1)! * Sum_{d|n, n/d odd} d.
MATHEMATICA
nmax = 21; CoefficientList[Series[Sum[ArcTanh[x^k], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
nmax = 21; CoefficientList[Series[-Log[EllipticTheta[4, 0, x]]/2, {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[(n - 1)! DivisorSum[n, # &, OddQ[n/#] &], {n, 1, 21}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 16 2019
STATUS
approved