OFFSET
0,3
FORMULA
G.f.: exp(Sum_{k>=1} (sigma_1(k) - 2*sigma_2(k))*x^k/k).
MAPLE
a:=series(mul((1-x^k)^(2*k-1), k=1..100), x=0, 44): seq(coeff(a, x, n), n=0..43); # Paolo P. Lava, Apr 02 2019
MATHEMATICA
nmax = 43; CoefficientList[Series[Product[(1 - x^k)^(2 k - 1), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 43; CoefficientList[Series[Exp[Sum[(DivisorSigma[1, k] - 2 DivisorSigma[2, k]) x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d (1 - 2 d), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 43}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Sep 25 2018
STATUS
approved