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
Keywords
Examples
a(18) = 3 because we have [15, 3], [13, 5] and [11, 7].
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
Programs
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Mathematica
nmax = 84; CoefficientList[Series[Product[1 + MoebiusMu[2 k - 1]^2 x^(2 k - 1), {k, 2, nmax}], {x, 0, nmax}], x]
Formula
G.f.: Product_{k>=2} (1 + mu(2*k-1)^2*x^(2*k-1)).
Comments