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A307075 Expansion of 1/(1 - Sum_{k>=1} mu(k)*x^k*(1 + x^k)/(1 - x^k)^3). 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Invert transform of A007434.

LINKS

Table of n, a(n) for n=0..28.

FORMULA

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

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}]

CROSSREFS

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

Sequence in context: A188716 A100506 A173414 * A219903 A238807 A240333

Adjacent sequences:  A307072 A307073 A307074 * A307076 A307077 A307078

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 22 2019

STATUS

approved

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Last modified May 18 08:30 EDT 2022. Contains 353785 sequences. (Running on oeis4.)