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A134538
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a(n) = 5*n^2 - 1.
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5
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4, 19, 44, 79, 124, 179, 244, 319, 404, 499, 604, 719, 844, 979, 1124, 1279, 1444, 1619, 1804, 1999, 2204, 2419, 2644, 2879, 3124, 3379, 3644, 3919, 4204, 4499, 4804, 5119, 5444, 5779, 6124, 6479, 6844, 7219, 7604, 7999, 8404, 8819, 9244, 9679, 10124
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OFFSET
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1,1
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COMMENTS
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For k != 0, the quintic polynomials of the form x^5 + 5*(5*k^2-1)*x + 4*(5*k^2-1) have Galois group A5 (order 60) over rational numbers.
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n) = (1 - (Pi/sqrt(5))*cot(Pi/sqrt(5)))/2.
Sum_{n>=1} (-1)^(n+1)/a(n) = ((Pi/sqrt(5))*csc(Pi/sqrt(5)) - 1)/2.
Product_{n>=1} (1 + 1/a(n)) = (Pi/sqrt(5))*csc(Pi/sqrt(5)).
Product_{n>=1} (1 - 1/a(n)) = csc(Pi/sqrt(5))*sin(sqrt(2/5)*Pi)/sqrt(2). (End)
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MATHEMATICA
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Table[5n^2 - 1, {n, 1, 50}]
CoefficientList[Series[(4+7*x-x^2)/(1-x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 09 2012 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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