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A162261
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a(n) = (2*n^3 + 5*n^2 - 7*n)/2.
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4
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0, 11, 39, 90, 170, 285, 441, 644, 900, 1215, 1595, 2046, 2574, 3185, 3885, 4680, 5576, 6579, 7695, 8930, 10290, 11781, 13409, 15180, 17100, 19175, 21411, 23814, 26390, 29145, 32085, 35216, 38544, 42075, 45815, 49770, 53946, 58349, 62985, 67860
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OFFSET
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1,2
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LINKS
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FORMULA
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Row sums from A155724: a(n) = Sum_{m=1..n} (2*m*n + m + n - 4).
G.f.: x^2*(11 - 5*x)/(1-x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
Sum_{n>=2} 1/a(n) = 8*log(2)/63 + 1166/19845.
Sum_{n>=2} (-1)^n/a(n) = (32*log(2) - 2*Pi - 3566/315)/63. (End)
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MATHEMATICA
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CoefficientList[Series[x*(11-5*x)/(1-x)^4, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 11, 39, 90}, 50](* Vincenzo Librandi, Mar 04 2012 *)
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PROG
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(Magma) [(2*n^3 + 5*n^2 - 7*n)/2 : n in [1..50]]; // Wesley Ivan Hurt, May 07 2021
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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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EXTENSIONS
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STATUS
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approved
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