A329275 Expansion of 1 / (1 + Sum_{k>=1} mu(k) * log(1 - 2 * x^k) / k), where mu = A008683.

1, 2, 5, 14, 40, 116, 336, 976, 2835, 8238, 23940, 69580, 202235, 587822, 1708606, 4966420, 14436034, 41961830, 121972548, 354544354, 1030574824, 2995634338, 8707595956, 25310916258, 73572844430, 213858876100, 621637274730, 1806952922994, 5252386090589, 15267448253302

Offset: 0

Author

Ilya Gutkovskiy, Nov 11 2019

Keywords

• nonn

Comments

Invert transform of A001037.

Crossrefs

Cf. A000079, A001037, A008683, A329276.

Programs

Maple

b:= proc(n) option remember; `if`(n=0, 1, (2^n-add(
      d*b(d), d=numtheory[divisors](n) minus {n}))/n)
    end:
a:= proc(n) option remember; `if`(n=0, 1,
      add(a(n-i)*b(i), i=1..n))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Nov 11 2019

Mathematica

nmax = 29; CoefficientList[Series[1/(1 + Sum[MoebiusMu[k] Log[1 - 2 x^k]/k, {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[(1/k) DivisorSum[k, MoebiusMu[#] 2^(k/#) &] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 29}]

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A001037(k) * a(n-k).