A307240 a(0) = 1; a(n) = Sum_{k=1..n} -lambda(k+1)*a(n-k), where lambda() is the Liouville function (A008836).

1, 1, 2, 2, 4, 4, 8, 10, 18, 22, 38, 50, 84, 114, 186, 256, 406, 570, 896, 1280, 1986, 2862, 4394, 6380, 9730, 14224, 21582, 31690, 47872, 70544, 106248, 157016, 235930, 349382, 523976, 777144, 1163882, 1728396, 2585802, 3843568, 5745510, 8546218, 12767232, 19001168

Offset

0,3

Links

Table of n, a(n) for n=0..43.

Formula

G.f.: x / Sum_{k>=1} lambda(k)*x^k.

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[-LiouvilleLambda[k + 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 43}]
nmax = 43; CoefficientList[Series[x/Sum[LiouvilleLambda[k] x^k, {k, 1, nmax + 1}], {x, 0, nmax}], x]

Crossrefs

Cf. A008836, A073776, A307076.

Sequence in context: A187213 A022476 A347206 * A000013 A064484 A063776

Adjacent sequences: A307237 A307238 A307239 * A307241 A307242 A307243

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 30 2019

Status

approved