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

Author

Ilya Gutkovskiy, Feb 06 2021

Keywords

• nonn

Crossrefs

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

Programs

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}]

Formula

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