A339220 Number of partitions of n into squarefree parts where every part appears at least 2 times.

1, 0, 1, 1, 2, 1, 4, 2, 5, 5, 8, 6, 13, 10, 17, 17, 24, 22, 36, 32, 47, 48, 64, 63, 90, 86, 116, 120, 154, 156, 208, 206, 265, 277, 344, 354, 448, 458, 566, 596, 720, 752, 920, 956, 1149, 1217, 1440, 1518, 1810, 1900, 2236, 2380, 2771, 2937, 3434, 3631, 4204, 4487, 5155, 5485, 6317

Offset

0,5

Links

Table of n, a(n) for n=0..60.

Index entries for sequences related to partitions

Formula

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

Example

a(6) = 4 because we have [3, 3], [2, 2, 2], [2, 2, 1, 1] and [1, 1, 1, 1, 1, 1].

Mathematica

nmax = 60; CoefficientList[Series[Product[1 + MoebiusMu[k]^2 x^(2 k)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A005117, A007690, A073576.

Sequence in context: A161241 A161026 A161077 * A161293 A328163 A217916

Adjacent sequences: A339217 A339218 A339219 * A339221 A339222 A339223

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 27 2020

Status

approved