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, 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

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