A329276 Expansion of 1 / (1 - Sum_{k>=1} mu(2*k) * log(1 - 2 * x^k) / (2 * k)), where mu = A008683.

1, 1, 2, 4, 9, 20, 45, 102, 232, 528, 1204, 2748, 6276, 14342, 32787, 74976, 171495, 392337, 897696, 2054232, 4701202, 10759689, 24627245, 56370546, 129034271, 295373313, 676158166, 1547869038, 3543458906, 8111974160, 18570800837, 42514665175, 97330789942, 222825306335

Offset: 0

Author

Ilya Gutkovskiy, Nov 11 2019

Keywords

• nonn

Comments

Invert transform of A000048.

Crossrefs

Cf. A000048, A008683, A123916, A329275.

Programs

Mathematica

nmax = 33; CoefficientList[Series[1/(1 - Sum[MoebiusMu[2 k] Log[1 - 2 x^k]/(2 k), {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[(1/(2 k)) DivisorSum[k, MoebiusMu[#] 2^(k/#) &, OddQ] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 33}]

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A000048(k) * a(n-k).