

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
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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(nk).


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



