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

Author

Ilya Gutkovskiy, Mar 30 2019

Keywords

• nonn

Crossrefs

Cf. A008836, A073776, A307076.

Programs

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]

Formula

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