A307657 G.f. A(x) satisfies: 1/(1 + x) = A(x)*A(x^2)^2*A(x^3)^3*A(x^4)^4* ... *A(x^k)^k* ...

1, -1, 3, 0, 1, 10, -13, 33, -24, 26, 22, -53, 148, -181, 233, -146, 69, 157, -373, 721, -884, 1071, -1076, 1041, -444, -425, 1767, -3225, 5232, -7144, 7942, -6920, 4999, -1112, -5947, 15481, -24273, 32103, -39255, 43839, -37560, 18235, 6158, -35079, 81689, -134919, 167667, -179256

Offset: 0

Author

Ilya Gutkovskiy, Apr 20 2019

Keywords

• sign

Comments

Convolution inverse of A307649.

Examples

			G.f.: A(x) = 1 - x + 3*x^2 + x^4 + 10*x^5 - 13*x^6 + 33*x^7 - 24*x^8 + 26*x^9 + 22*x^10 - 53*x^11 + 148*x^12 - 181*x^13 + ...
		

Crossrefs

Cf. A008683, A055615, A117211, A307649.

Programs

Mathematica

terms = 47; CoefficientList[Series[Product[1/(1 + x^k)^(MoebiusMu[k] k), {k, 1, terms}], {x, 0, terms}], x]
terms = 47; A[] = 1; Do[A[x] = 1/((1 + x) Product[A[x^k]^k, {k, 2, terms}]) + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x]

Formula

G.f.: Product_{k>=1} 1/(1 + x^k)^(mu(k)*k).