A307075 Expansion of 1/(1 - Sum_{k>=1} mu(k)*x^k*(1 + x^k)/(1 - x^k)^3).

1, 1, 4, 15, 47, 160, 517, 1721, 5668, 18687, 61687, 203448, 671253, 2214377, 7305308, 24100319, 79506903, 262294336, 865310405, 2854666385, 9417565852, 31068622271, 102495625503, 338133855032, 1115506197957, 3680063534409, 12140557957708, 40051794232519, 132131177728807

Offset: 0

Author

Ilya Gutkovskiy, Mar 22 2019

Keywords

• nonn

Comments

Invert transform of A007434.

Crossrefs

Cf. A007434, A008683, A159929, A301875, A301876.

Programs

Mathematica

nmax = 28; CoefficientList[Series[1/(1 - Sum[MoebiusMu[k] x^k (1 + x^k)/(1 - x^k)^3, {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[Sum[MoebiusMu[k/d] d^2, {d, Divisors[k]}] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 28}]

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A007434(k)*a(n-k).