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A284835 Expansion of Sum_{i>=1} mu(i)^2*x^i/(1 - x^i) * Product_{j=1..i} 1/(1 - mu(j)^2*x^j), where mu() is the Moebius function (A008683). 0
1, 3, 5, 8, 11, 18, 22, 31, 39, 53, 64, 87, 104, 134, 165, 205, 248, 310, 368, 455, 545, 659, 784, 947, 1117, 1337, 1579, 1872, 2197, 2604, 3036, 3570, 4168, 4866, 5661, 6599, 7633, 8859, 10236, 11831, 13625, 15715, 18036, 20728, 23761, 27211, 31106, 35560, 40533, 46221, 52596, 59813, 67912, 77090, 87343 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Total number of largest parts in all partitions of n into squarefree parts (A005117)

LINKS

Table of n, a(n) for n=1..55.

Index entries for related partition-counting sequences

FORMULA

G.f.: Sum_{i>=1} mu(i)^2*x^i/(1 - x^i) * Product_{j=1..i} 1/(1 - mu(j)^2*x^j).

EXAMPLE

a(5) = 11 because we have [5], [3, 2], [3, 1, 1], [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1] and 1 + 1 + 1 + 2 + 1 + 5 = 11.

MATHEMATICA

nmax = 55; Rest[CoefficientList[Series[Sum[MoebiusMu[i]^2 x^i/(1 - x^i) Product[1/(1 - MoebiusMu[j]^2 x^j), {j, 1, i}], {i, 1, nmax}], {x, 0, nmax}], x]]

PROG

(PARI) x='x+O('x^56); Vec(sum(i=1, 56, moebius(i)^2*x^i/(1 - x^i) * prod(j=1, i, 1/(1 - moebius(j)^2*x^j)))) \\ Indranil Ghosh, Apr 04 2017

CROSSREFS

Cf. A005117, A008683, A046746, A073576, A092311, A281572, A284829.

Sequence in context: A281333 A244031 A194803 * A308266 A320594 A227563

Adjacent sequences:  A284832 A284833 A284834 * A284836 A284837 A284838

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 03 2017

STATUS

approved

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Last modified July 21 07:23 EDT 2019. Contains 325192 sequences. (Running on oeis4.)