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A280169 Expansion of Product_{k>=2} 1/(1 - mu(2*k-1)^2*x^(2*k-1)), where mu() is the Moebius function (A008683). 1
1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 6, 6, 8, 9, 10, 11, 13, 14, 17, 18, 21, 24, 26, 30, 33, 38, 42, 47, 53, 58, 65, 73, 80, 90, 99, 110, 122, 134, 149, 164, 181, 199, 220, 242, 266, 292, 321, 352, 386, 424, 463, 507, 554, 606, 662, 722, 788, 860, 936, 1020, 1111, 1208, 1314, 1428, 1553, 1685, 1829, 1984, 2152 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

COMMENTS

Number of partitions of n into odd squarefree parts > 1.

LINKS

Table of n, a(n) for n=0..76.

Joerg Arndt, Matters Computational (The Fxtbook), section 16.4.3 "Partitions into square-free parts", pp.351-352

Eric Weisstein's World of Mathematics, Squarefree

Index entries for related partition-counting sequences

FORMULA

G.f.: Product_{k>=2} 1/(1 - mu(2*k-1)^2*x^(2*k-1)).

EXAMPLE

a(13) = 3 because we have [13], [7, 3, 3] and [5, 5, 3].

MATHEMATICA

nmax = 76; CoefficientList[Series[Product[1/(1 - MoebiusMu[2 k - 1]^2 x^(2 k - 1)), {k, 2, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A005117, A008683, A056911, A073576, A134345, A144338, A280127.

Sequence in context: A288122 A060970 A035429 * A018117 A086936 A214129

Adjacent sequences:  A280166 A280167 A280168 * A280170 A280171 A280172

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 27 2016

STATUS

approved

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Last modified October 30 03:24 EDT 2020. Contains 338076 sequences. (Running on oeis4.)