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A280716 Expansion of Product_{k>=2} (1 + mu(2*k-1)^2*x^(2*k-1)), where mu() is the Moebius function (A008683). 0
1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 1, 3, 2, 3, 3, 3, 4, 4, 3, 5, 4, 5, 6, 4, 8, 6, 8, 8, 9, 11, 10, 11, 14, 13, 14, 15, 16, 19, 16, 20, 22, 22, 23, 26, 29, 30, 31, 35, 39, 38, 43, 44, 49, 50, 52, 58, 59, 64, 67, 71, 77, 82, 85, 93, 97, 107, 108, 117, 125, 131, 138, 143, 157, 162, 168, 179, 194, 199 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,16

COMMENTS

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

LINKS

Table of n, a(n) for n=0..84.

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 + mu(2*k-1)^2*x^(2*k-1)).

EXAMPLE

a(18) = 3 because we have [15, 3], [13, 5] and [11, 7].

MATHEMATICA

nmax = 84; CoefficientList[Series[Product[1 + MoebiusMu[2 k - 1]^2 x^(2 k - 1), {k, 2, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A005117, A008683, A056911, A073576, A134337, A144338, A280128, A280169.

Sequence in context: A329949 A333867 A030717 * A319444 A071285 A289438

Adjacent sequences:  A280713 A280714 A280715 * A280717 A280718 A280719

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 07 2017

STATUS

approved

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Last modified October 15 16:06 EDT 2021. Contains 348033 sequences. (Running on oeis4.)