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, 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.

Links

Table of n, a(n) for n=0..67.

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

Cf. A008683, A117209, A117210, A307659.

Sequence in context: A286550 A366282 A364258 * A265511 A081236 A338896

Adjacent sequences: A307655 A307656 A307657 * A307659 A307660 A307661

Keyword

sign

Author

Ilya Gutkovskiy, Apr 20 2019

Status

approved