A307076 Expansion of 1/(1 - Sum_{k>=1} lambda(k)*x^k), where lambda() is the Liouville function (A008836).

1, 1, 0, -2, -2, 0, 4, 4, -2, -10, -6, 10, 22, 4, -34, -46, 16, 102, 86, -100, -272, -126, 370, 650, 60, -1138, -1384, 526, 3142, 2532, -2936, -7952, -3440, 10802, 18426, 596, -33344, -38418, 18716, 91934, 68400, -93402, -230962, -86236, 330144, 528880, -17298, -996040

Offset: 0

Author

Ilya Gutkovskiy, Mar 22 2019

Keywords

• sign

Comments

Invert transform of A008836.

Crossrefs

Cf. A008836, A118206, A118207, A300663.

Programs

Mathematica

nmax = 47; CoefficientList[Series[1/(1 - Sum[LiouvilleLambda[k] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[LiouvilleLambda[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 47}]

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A008836(k)*a(n-k).