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

Author

Ilya Gutkovskiy, Dec 27 2016

Keywords

• nonn

Comments

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

Examples

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

Links

• 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

Crossrefs

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

Programs

Mathematica

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

Formula

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