A307073 Expansion of 1/(1 - Sum_{k>=1} mu(k)^2*x^k/(1 - x^k)^2).

1, 1, 4, 11, 33, 94, 279, 803, 2348, 6823, 19879, 57834, 168405, 490125, 1426824, 4153197, 12089787, 35191868, 102440785, 298194567, 868017488, 2526715121, 7355031727, 21409798576, 62321907805, 181413177769, 528076639862, 1537181201003, 4474589318797, 13025106833162, 37914855831345

Offset: 0

Author

Ilya Gutkovskiy, Mar 22 2019

Keywords

• nonn

Comments

Invert transform of A001615.

Crossrefs

Cf. A001615, A008683, A156303, A159929, A301594.

Programs

Mathematica

nmax = 30; CoefficientList[Series[1/(1 - Sum[MoebiusMu[k]^2 x^k/(1 - x^k)^2, {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[DirichletConvolve[j, MoebiusMu[j]^2, j, k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 30}]

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A001615(k)*a(n-k).