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A319669
Expansion of Product_{k>=1} (1 - x^k)^(2*k-1).
0
1, -1, -3, -2, 1, 10, 13, 15, -1, -30, -63, -89, -80, -14, 131, 304, 493, 561, 434, -32, -836, -1895, -2960, -3583, -3240, -1338, 2401, 8004, 14499, 20494, 23369, 20401, 8567, -13741, -46408, -85717, -124027, -149612, -147167, -101002, 2520, 168026, 388077, 634914
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}]
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Sep 25 2018
STATUS
approved