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A327799
Expansion of 1 / (1 + Sum_{i>=1} Sum_{j=1..i} x^(i*j)).
0
1, -1, 0, 0, -1, 2, -2, 2, -1, -2, 5, -6, 5, -1, -5, 10, -14, 14, -5, -10, 26, -38, 36, -15, -20, 60, -91, 93, -51, -33, 138, -223, 237, -145, -52, 307, -528, 596, -412, -43, 674, -1258, 1492, -1126, 84, 1442, -2938, 3687, -3034, 680, 3000, -6818, 9050, -7997
OFFSET
0,6
FORMULA
G.f.: 1 / (1 + Sum_{k>=1} x^(k^2) / (1 - x^k)).
a(0) = 1; a(n) = -Sum_{k=1..n} A038548(k) * a(n-k).
MATHEMATICA
nmax = 53; CoefficientList[Series[1/(1 + Sum[x^(k^2)/(1 - x^k), {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = -Sum[Floor[(DivisorSigma[0, k] + 1)/2] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 53}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Sep 25 2019
STATUS
approved