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A329276 Expansion of 1 / (1 - Sum_{k>=1} mu(2*k) * log(1 - 2 * x^k) / (2 * k)), where mu = A008683. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Invert transform of A000048.

LINKS

Table of n, a(n) for n=0..33.

FORMULA

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

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}]

CROSSREFS

Cf. A000048, A008683, A123916, A329275.

Sequence in context: A227978 A206741 A167750 * A308435 A188460 A111099

Adjacent sequences:  A329272 A329274 A329275 * A329278 A329279 A329280

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 11 2019

STATUS

approved

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Last modified December 5 20:54 EST 2019. Contains 329779 sequences. (Running on oeis4.)