A356907 Expansion of 1 / (1 + Sum_{k>=1} lambda(k)*x^k), where lambda() is the Liouville function (A008836).

1, -1, 2, -2, 2, 0, -4, 12, -22, 34, -42, 38, -6, -68, 202, -394, 616, -782, 730, -204, -1104, 3486, -6994, 11142, -14452, 14026, -5296, -17558, 60042, -123860, 201128, -266384, 268176, -124034, -273626, 1030396, -2188864, 3624290, -4898740, 5101306, -2744408

Offset

0,3

Links

Table of n, a(n) for n=0..40.

Formula

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

Mathematica

nmax = 40; 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, 40}]

Crossrefs

Cf. A008836, A118205, A118206, A118207, A118208, A185694, A307076, A307240.

Sequence in context: A215461 A158851 A151930 * A084203 A073358 A124342

Adjacent sequences: A356904 A356905 A356906 * A356908 A356909 A356910

Keyword

sign

Author

Ilya Gutkovskiy, Oct 02 2022

Status

approved