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A346165
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Number of n X n invertible matrices whose characteristic polynomial is squarefree.
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1
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1, 1, 2, 104, 9792, 4887552, 10456694784, 80831009783808, 2695921347430711296, 347083584759711311855616, 184330749741189300682890412032, 383205061911277693825526401937178624, 3224343525101169010615339144085384529444864, 107976295438859678148286176040509108456782680817664
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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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Sum_{n>=0} a(n)*x^n/A002884(n) = (1 + x) * Product_{n>=2} (1 + x^n/(2^n -1))^A001037(n)
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MATHEMATICA
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nn = 13; A001037 = Table[1/n Sum[MoebiusMu[n/d] 2^d, {d, Divisors[n]}], {n, 1, nn}]; Table[Product[2^n - 2^i, {i, 0, n - 1}], {n, 0, nn}] CoefficientList[
Series[(1 + x) Product[(1 + x^i/(2^i - 1))^A001037[[i]], {i, 2, nn}], {x, 0, nn}], x]
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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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