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A022997
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Numerator of n*(n-2)*(2*n-1)/(2*(n-1)).
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1
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0, 15, 28, 135, 132, 455, 360, 1071, 760, 2079, 1380, 3575, 2268, 5655, 3472, 8415, 5040, 11951, 7020, 16359, 9460, 21735, 12408, 28175, 15912, 35775, 20020, 44631, 24780, 54839, 30240, 66495, 36448, 79695, 43452, 94535, 51300, 111111, 60040, 129519, 69720, 149855
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OFFSET
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2,2
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LINKS
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FORMULA
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G.f.: x^3*(x^6+5x^4+20x^3+75x^2+28x+15)/((x-1)^4*(x+1)^4). - Ralf Stephan, Sep 03 2003
Sum_{n>=3} 1/a(n) = 11/9 + Pi/6 - 7*log(2)/3. - Amiram Eldar, Sep 21 2023
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EXAMPLE
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Fractions begins with 0, 15/4, 28/3, 135/8, 132/5, 455/12, 360/7, 1071/16, 760/9, 2079/20, 1380/11, 3575/24, ...
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MATHEMATICA
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a[n_] := Numerator[n*(n - 2)*(2*n - 1)/(2*(n - 1))]; Array[a, 50, 2] (* Amiram Eldar, Sep 21 2023 *)
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PROG
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(PARI) a(n) = numerator(n*(n-2)*(2*n-1)/(2*(n-1))); \\ Amiram Eldar, Sep 21 2023
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CROSSREFS
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Cf. A022998 (denominators, with an offset shift).
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KEYWORD
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nonn,easy,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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