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%I #43 Feb 05 2024 02:26:23
%S 7,8,11,16,23,32,43,56,71,88,107,128,151,176,203,232,263,296,331,368,
%T 407,448,491,536,583,632,683,736,791,848,907,968,1031,1096,1163,1232,
%U 1303,1376,1451,1528,1607,1688,1771,1856,1943,2032,2123,2216,2311,2408
%N a(n) = n^2 + 7.
%H Ivan Panchenko, <a href="/A117619/b117619.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: (-8*x^2 + 13*x - 7)/(x - 1)^3. - _Indranil Ghosh_, Apr 05 2017
%F From _Amiram Eldar_, Nov 02 2020: (Start)
%F Sum_{n>=0} 1/a(n) = (1 + sqrt(7)*Pi*coth(sqrt(7)*Pi))/14.
%F Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(7)*Pi*cosech(sqrt(7)*Pi))/14. (End)
%F From _Amiram Eldar_, Feb 05 2024: (Start)
%F Product_{n>=0} (1 - 1/a(n)) = sqrt(6/7)*sinh(sqrt(6)*Pi)/sinh(sqrt(7)*Pi).
%F Product_{n>=0} (1 + 1/a(n)) = 2*sqrt(2/7)*sinh(2*sqrt(2)*Pi)/sinh(sqrt(7)*Pi). (End)
%t Table[n^2 + 7, {n, 0, 60}] (* _Stefan Steinerberger_, Apr 08 2006 *)
%o (PARI) a(n) = n^2 + 7 \\ _Indranil Ghosh_, Apr 05 2017
%o (Python) def a(n): return n**2 + 7 # _Indranil Ghosh_, Apr 05 2017
%Y Cf. A117951, A117950.
%K nonn,less,easy
%O 0,1
%A _Parthasarathy Nambi_, Apr 07 2006
%E More terms from _Stefan Steinerberger_, Apr 08 2006
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