A307649 G.f. A(x) satisfies: (1 + x) = A(x)*A(x^2)^2*A(x^3)^3*A(x^4)^4* ... *A(x^k)^k* ...

1, 1, -2, -5, 0, 4, 9, 2, -10, -21, 29, 15, -18, -80, 50, 59, 207, -228, -244, -315, 868, 103, 360, -1907, 752, -151, 3802, -5032, 965, -5279, 13742, -6049, 9107, -33835, 25398, -15098, 63365, -79614, 51752, -117194, 196980, -156321, 209085, -435223, 463497, -441950, 871202, -1146187, 1023944, -1704179

Offset

0,3

Comments

Weigh transform of A055615.

Links

Table of n, a(n) for n=0..49.

Formula

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

Example

G.f.: A(x) = 1 + x - 2*x^2 - 5*x^3 + 4*x^5 + 9*x^6 + 2*x^7 - 10*x^8 - 21*x^9 + 29*x^10 + 15*x^11 - 18*x^12 - 80*x^13 + ...

Mathematica

terms = 49; CoefficientList[Series[Product[(1 + x^k)^(MoebiusMu[k] k), {k, 1, terms}], {x, 0, terms}], x]
terms = 49; A[_] = 1; Do[A[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, A117210, A307648.

Sequence in context: A112695 A215078 A067881 * A024714 A123342 A196816

Adjacent sequences: A307646 A307647 A307648 * A307650 A307651 A307652

Keyword

sign

Author

Ilya Gutkovskiy, Apr 19 2019

Status

approved