A307659 G.f. A(x) satisfies: (1 + x)/(1 - x) = A(x)*A(x^2)^2*A(x^3)^3*A(x^4)^4* ... *A(x^k)^k* ...

1, 2, -2, -12, -10, 12, 44, 40, -26, -132, -60, 104, 156, -152, -136, 80, 1030, 204, -1548, -3736, 1780, 5096, 7496, -8208, -9956, -11416, 30824, 2784, -296, -72768, 62032, 22752, 157126, -290356, -41420, -244296, 896996, -285896, 436040, -2139120, 1661940, -1028632, 4535608, -6487744, 4125224

Offset

0,2

Comments

Convolution of A307648 and A307649.

Links

Table of n, a(n) for n=0..44.

Formula

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

Example

G.f.: A(x) = 1 + 2*x - 2*x^2 - 12*x^3 - 10*x^4 + 12*x^5 + 44*x^6 + 40*x^7 - 26*x^8 - 132*x^9 - 60*x^10 + ...

Mathematica

terms = 44; CoefficientList[Series[Product[((1 + x^k)/(1 - x^k))^(MoebiusMu[k] k), {k, 1, terms}], {x, 0, terms}], x]
terms = 44; A[_] = 1; Do[A[x_] = (1 + x)/((1 - x) Product[A[x^k]^k, {k, 2, terms}]) + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A008683, A055615, A307648, A307649, A307658.

Sequence in context: A279504 A279994 A350784 * A327874 A190295 A228154

Adjacent sequences: A307656 A307657 A307658 * A307660 A307661 A307662

Keyword

sign

Author

Ilya Gutkovskiy, Apr 20 2019

Status

approved