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%I #35 Jan 15 2021 07:37:19
%S 0,9,22,39,60,85,114,147,184,225,270,319,372,429,490,555,624,697,774,
%T 855,940,1029,1122,1219,1320,1425,1534,1647,1764,1885,2010,2139,2272,
%U 2409,2550,2695,2844,2997,3154,3315,3480,3649,3822,3999,4180,4365
%N a(n) = (n-1)*(2*n+5).
%C Old name was: "Ratio of Sum of k^2-1 to sum of k made into an integer sequence: (n-1)*(2*n+5)".
%H G. C. Greubel, <a href="/A130861/b130861.txt">Table of n, a(n) for n = 1..5000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 3*(n + 1)*( Sum_{k=1..n} k^2-1 )/ ( Sum_{k=1..n} k ) = (-1 + n)*(5 + 2*n).
%F G.f.: x^2*(9 - 5*x)/(1-x)^3. - _R. J. Mathar_, Nov 14 2007
%F a(n) = a(n-1) +4*n +1 for n>1, a(1)=0. - _Vincenzo Librandi_, Nov 23 2010
%F a(n) = n*(2n+7) with offset 0. - _Michel Marcus_, Jan 28 2015
%F 8*a(n) + 49 = A016838(n). - _Bruno Berselli_, Jan 28 2015
%F E.g.f.: 5 + (2*x^2 + 5* x -5)*exp(x). - _G. C. Greubel_, Jul 21 2017
%t Table[(n-1)(2n+5),{n,50}] (* or *) LinearRecurrence[{3,-3,1},{0,9,22},50] (* _Harvey P. Dale_, Oct 02 2015 *)
%o (PARI) a(n)=(n-1)*(2*n+5) \\ _Charles R Greathouse IV_, Sep 24 2015
%Y Cf. A016838.
%K nonn,easy
%O 1,2
%A _Roger L. Bagula_, Jul 22 2007
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