This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A199300 #30 Mar 26 2025 17:23:29
%S A199300 1,21,245,2401,21609,184877,1529437,12353145,98001617,766718533,
%T A199300 5931980229,45478515089,346032180025,2616003280989,19668469112621,
%U A199300 147174406808233,1096686708796833,8142067989552245,60251303122686613,444556912229552577,3271482918202092041
%N A199300 a(n) = (2*n + 1)*7^n.
%H A199300 Vincenzo Librandi, <a href="/A199300/b199300.txt">Table of n, a(n) for n = 0..1000</a>
%H A199300 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-49).
%F A199300 a(n) = 14*a(n-1) - 49*a(n-2).
%F A199300 G.f.: (1+7*x)/(1-7*x)^2.
%F A199300 a(n) = 7*a(n-1) + 2*7^n. - _Vincenzo Librandi_, Nov 05 2011
%F A199300 From _Amiram Eldar_, Dec 10 2022: (Start)
%F A199300 Sum_{n>=0} 1/a(n) = sqrt(7)*arccoth(sqrt(7)).
%F A199300 Sum_{n>=0} (-1)^n/a(n) = sqrt(7)*arccot(sqrt(7)). (End)
%F A199300 E.g.f.: exp(7*x)*(1 + 14*x). - _Stefano Spezia_, May 09 2023
%t A199300 a[n_] := (2*n + 1)*7^n; Array[a, 25, 0] (* _Amiram Eldar_, Dec 10 2022 *)
%t A199300 LinearRecurrence[{14,-49},{1,21},30] (* _Harvey P. Dale_, Mar 26 2025 *)
%o A199300 (Magma) [(2*n+1)*7^n: n in [0..30]]; // _Vincenzo Librandi_, Nov 05 2011
%o A199300 (PARI) a(n) = (2*n+1)*7^n \\ _Amiram Eldar_, Dec 10 2022
%Y A199300 Cf. A014480, A058962, A124647, A155988, A171220, A199299, A199301.
%K A199300 nonn,easy
%O A199300 0,2
%A A199300 _Philippe Deléham_, Nov 04 2011
%E A199300 a(15) corrected by _Vincenzo Librandi_, Nov 05 2011