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A103619
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Number of permutations of n elements admitting a cube root.
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8
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1, 1, 2, 4, 16, 80, 400, 2800, 22400, 181440, 1814400, 19958400, 218803200, 2844441600, 39822182400, 556972416000, 8911558656000, 151496497152000, 2579172973977600, 49004286505574400, 980085730111488000, 19584861165821952000, 430866945648082944000
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OFFSET
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0,3
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LINKS
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FORMULA
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E.g.f.: (1-x^3)^(1/3)/(1-x)*Product(1/3*exp(1/3*x^(3*m)/m)+2/3*exp(-1/6*x^(3*m)/m)*cos(1/6*3^(1/2)*x^(3*m)/m), m = 1 .. infinity).
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MAPLE
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with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(`if`(irem(j, igcd(i, 3))<>0, 0, (i-1)!^j*
multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1)), j=0..n/i)))
end:
a:= n-> b(n$2):
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MATHEMATICA
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CoefficientList[Series[(1-x^3)^(1/3)/(1-x) * Product[1/3*E^(1/3*x^(3*m)/m) + 2/3*E^(-1/6*x^(3*m)/m) * Cos[1/6*3^(1/2)*x^(3*m)/m], {m, 1, 20}], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Sep 13 2014 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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