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A098850 a(n) = n*(n + 18).

%I A098850 #29 Jan 16 2021 04:23:02
%S A098850 0,19,40,63,88,115,144,175,208,243,280,319,360,403,448,495,544,595,
%T A098850 648,703,760,819,880,943,1008,1075,1144,1215,1288,1363,1440,1519,1600,
%U A098850 1683,1768,1855,1944,2035,2128,2223,2320,2419,2520,2623,2728,2835,2944,3055
%N A098850 a(n) = n*(n + 18).
%H A098850 G. C. Greubel, <a href="/A098850/b098850.txt">Table of n, a(n) for n = 0..1000</a>
%H A098850 Felix P. Muga II, <a href="https://www.researchgate.net/publication/267327689_Extending_the_Golden_Ratio_and_the_Binet-de_Moivre_Formula">Extending the Golden Ratio and the Binet-de Moivre Formula</a>, Preprint on ResearchGate, March 2014.
%H A098850 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A098850 a(n) = (n+9)^2 - 9^2 = n*(n + 18), n>=0.
%F A098850 G.f.: x*(19 - 17*x)/(1-x)^3.
%F A098850 a(n) = 2*n + a(n-1) + 17 (with a(0)=0). - _Vincenzo Librandi_, Nov 17 2010
%F A098850 From _G. C. Greubel_, Jul 29 2016: (Start)
%F A098850 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A098850 E.g.f.: x*(19 + x)*exp(x). (End)
%F A098850 From _Amiram Eldar_, Jan 16 2021: (Start)
%F A098850 Sum_{n>=1} 1/a(n) = H(18)/18 = A001008(18)/A102928(18) = 14274301/73513440, where H(k) is the k-th harmonic number.
%F A098850 Sum_{n>=1} (-1)^(n+1)/a(n) = 1632341/44108064. (End)
%p A098850 seq(n*(n+18),n=0..52); # _Emeric Deutsch_, Mar 06 2005
%t A098850 LinearRecurrence[{3, -3, 1}, {0, 19, 40}, 25] (* _G. C. Greubel_, Jul 29 2016 *)
%o A098850 (PARI) a(n)=n*(n+18) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A098850 Cf. A001008, A098832, A102928.
%Y A098850 a(n-9), n>=10, ninth column (used for the n=9 series of the hydrogen atom) of triangle A120070.
%K A098850 nonn,easy
%O A098850 0,2
%A A098850 Eugene McDonnell (eemcd(AT)mac.com), Nov 04 2004
%E A098850 More terms from _Emeric Deutsch_, Mar 06 2005