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A111396
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a(n) = n*(n+7)*(n+8)/6.
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6
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0, 12, 30, 55, 88, 130, 182, 245, 320, 408, 510, 627, 760, 910, 1078, 1265, 1472, 1700, 1950, 2223, 2520, 2842, 3190, 3565, 3968, 4400, 4862, 5355, 5880, 6438, 7030, 7657, 8320, 9020, 9758, 10535, 11352, 12210, 13110, 14053, 15040, 16072, 17150, 18275, 19448
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: x*(12 - 18*x + 7*x^2) /(x-1)^4. - R. J. Mathar, Mar 15 2011
E.g.f.: (x/6)*(72 + 18*x + x^2)*exp(x). - G. C. Greubel, Jul 30 2022
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MAPLE
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[seq(binomial(n, 3)-2*binomial(n, 2), n=8..52)]; # Zerinvary Lajos, Nov 25 2006
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MATHEMATICA
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CoefficientList[Series[x*(12-18*x+7*x^2)/(x-1)^4, {x, 0, 50}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 12, 30, 55}, 40] (* Vincenzo Librandi, Jun 27 2012 *)
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PROG
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(Magma) I:=[0, 12, 30, 55]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 27 2012
(SageMath) [n*(n+7)*(n+8)/6 for n in (0..50)] # G. C. Greubel, Jul 30 2022
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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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