A280716 Expansion of Product_{k>=2} (1 + mu(2*k-1)^2*x^(2*k-1)), where mu() is the Moebius function (A008683).

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

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