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A079027
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a(n) = det(M(n)) where M(n) is the n X n matrix defined by m(i,i)=6, m(i,j)=i/j.
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2
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6, 35, 200, 1125, 6250, 34375, 187500, 1015625, 5468750, 29296875, 156250000, 830078125, 4394531250, 23193359375, 122070312500, 640869140625, 3356933593750, 17547607421875, 91552734375000, 476837158203125, 2479553222656250, 12874603271484375
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = (n+5)*5^(n-1).
a(n) = 10*a(n-1)-25*a(n-2). G.f.: -x*(25*x-6) / (5*x-1)^2. - Colin Barker, Jun 18 2013
Sum_{n>=1} 1/a(n) = 15625*log(5/4) - 41837/12.
Sum_{n>=1} (-1)^(n+1)/a(n) = 34187/12 - 15625*log(6/5). (End)
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MAPLE
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MATHEMATICA
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LinearRecurrence[{10, -25}, {6, 35}, 30] (* Harvey P. Dale, Jun 14 2022 *)
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PROG
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(PARI) a(n) = matdet(matrix(n, n, i, j, if(i==j, 6, i/j))); \\ Michel Marcus, Nov 30 2013
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CROSSREFS
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KEYWORD
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nonn,easy,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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