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A307658
G.f. A(x) satisfies: (1 + x)/(1 - x) = A(x)*A(x^2)*A(x^3)*A(x^4)* ... *A(x^k)* ...
1
1, 2, 0, -4, -4, 0, 4, 4, 0, -4, 0, 4, 0, -8, -4, 8, 16, 0, -20, -20, 8, 24, 20, -12, -24, -8, 24, 4, -16, -24, 16, 28, 24, -40, -32, 0, 72, 24, -28, -104, 0, 48, 88, -44, -32, -64, 92, 20, 24, -124, 64, 0, 96, -168, -12, -72, 272, -24, 72, -300, 104, -88, 316, -272, 128, -272, 376, -300
OFFSET
0,2
COMMENTS
Convolution of A117209 and A117210.
FORMULA
G.f.: Product_{k>=1} ((1 + x^k)/(1 - x^k))^mu(k).
EXAMPLE
G.f.: A(x) = 1 + 2*x - 4*x^3 - 4*x^4 + 4*x^6 + 4*x^7 - 4*x^9 + 4*x^11 - 8*x^13 - 4*x^14 + 8*x^15 + ...
MATHEMATICA
terms = 67; CoefficientList[Series[Product[((1 + x^k)/(1 - x^k))^MoebiusMu[k], {k, 1, terms}], {x, 0, terms}], x]
terms = 67; A[_] = 1; Do[A[x_] = (1 + x)/((1 - x) Product[A[x^k], {k, 2, terms}]) + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Apr 20 2019
STATUS
approved