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%I A072173 #12 Sep 08 2022 08:45:06
%S A072173 239,40955757,3899056325995,311805194956024553,
%T A072173 22899374409963958061031,1598709646931895970271741029,
%U A072173 107923510786468980575690686466147,7113114068808339968612339655730133985,460482613887654678993386180604955781138143,29397724727626925615108413436728112018437968221
%N A072173 a(n) = (2*n+1)*239^(2*n+1).
%C A072173 J. Machin (died 1751) used Pi/4 = 4*Sum_{n=0..inf} (-1)^n/((2*n+1)*5^(2*n+1)) - Sum_{n=0..inf} (-1)^n/((2*n+1)*239^(2*n+1)) to calculate Pi to 100 decimal places.
%D A072173 H. Doerrie, 100 Great Problems of Elementary Mathematics, Dover, NY, 1965, p. 73
%H A072173 Colin Barker, <a href="/A072173/b072173.txt">Table of n, a(n) for n = 0..200</a>
%H A072173 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (114242,-3262808641).
%F A072173 From _Colin Barker_, Aug 25 2016: (Start)
%F A072173 a(n) = 114242*a(n-1) - 3262808641*a(n-2) for n>1.
%F A072173 G.f.: 239*(1+57121*x) / (1-57121*x)^2. (End)
%F A072173 E.g.f.: m*(1+2*m^2*x)*exp(m^2*x), where m=239. - _G. C. Greubel_, Aug 26 2019
%p A072173 seq((2*n+1)*239^(2*n+1), n = 0..10); # _G. C. Greubel_, Aug 26 2019
%t A072173 Table[(2*n+1)*239^(2*n+1), {n,0,10}] (* _G. C. Greubel_, Aug 26 2019 *)
%o A072173 (PARI) Vec(239*(1+57121*x)/(1-57121*x)^2 + O(x^10)) \\ _Colin Barker_, Aug 25 2016
%o A072173 (PARI) vector(10, n, (2*n-1)*239^(2*n-1)) \\ _G. C. Greubel_, Aug 26 2019
%o A072173 (Magma) [(2*n+1)*239^(2*n+1): n in [0..10]]; // _G. C. Greubel_, Aug 26 2019
%o A072173 (Sage) [(2*n+1)*239^(2*n+1) for n in (0..10)] # _G. C. Greubel_, Aug 26 2019
%o A072173 (GAP) List([0..10]. n-> (2*n+1)*239^(2*n+1)); # _G. C. Greubel_, Aug 26 2019
%Y A072173 Cf. A072172.
%Y A072173 Cf. A157332. - _Jaume Oliver Lafont_, Mar 03 2009
%K A072173 nonn,easy
%O A072173 0,1
%A A072173 _N. J. A. Sloane_, Jun 30 2002

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