A341153 Number of partitions of 2*n into exactly n squarefree parts.

1, 1, 2, 2, 4, 5, 8, 9, 13, 16, 23, 27, 37, 44, 59, 70, 91, 107, 138, 162, 205, 240, 300, 350, 432, 504, 615, 715, 865, 1003, 1206, 1394, 1663, 1918, 2276, 2618, 3088, 3544, 4160, 4764, 5566, 6360, 7401, 8440, 9779, 11131, 12854, 14602, 16803, 19051, 21859, 24741, 28303

Offset

0,3

Links

Table of n, a(n) for n=0..52.

Formula

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

Mathematica

nmax = 52; CoefficientList[Series[Product[1/(1 - MoebiusMu[k + 1]^2 x^k), {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d MoebiusMu[d + 1]^2, {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 52}]

Crossrefs

Cf. A005117, A008683, A073576, A341071, A341154.

Sequence in context: A326443 A326522 A326626 * A326628 A326524 A326629

Adjacent sequences: A341150 A341151 A341152 * A341154 A341155 A341156

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 06 2021

Status

approved