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A341153 Number of partitions of 2*n into exactly n squarefree parts. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 14 10:58 EDT 2022. Contains 356116 sequences. (Running on oeis4.)