OFFSET
0,1
COMMENTS
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.
REFERENCES
H. Doerrie, 100 Great Problems of Elementary Mathematics, Dover, NY, 1965, p. 73
LINKS
Colin Barker, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (114242,-3262808641).
FORMULA
From Colin Barker, Aug 25 2016: (Start)
a(n) = 114242*a(n-1) - 3262808641*a(n-2) for n>1.
G.f.: 239*(1+57121*x) / (1-57121*x)^2. (End)
E.g.f.: m*(1+2*m^2*x)*exp(m^2*x), where m=239. - G. C. Greubel, Aug 26 2019
MAPLE
seq((2*n+1)*239^(2*n+1), n = 0..10); # G. C. Greubel, Aug 26 2019
MATHEMATICA
Table[(2*n+1)*239^(2*n+1), {n, 0, 10}] (* G. C. Greubel, Aug 26 2019 *)
PROG
(PARI) Vec(239*(1+57121*x)/(1-57121*x)^2 + O(x^10)) \\ Colin Barker, Aug 25 2016
(PARI) vector(10, n, (2*n-1)*239^(2*n-1)) \\ G. C. Greubel, Aug 26 2019
(Magma) [(2*n+1)*239^(2*n+1): n in [0..10]]; // G. C. Greubel, Aug 26 2019
(Sage) [(2*n+1)*239^(2*n+1) for n in (0..10)] # G. C. Greubel, Aug 26 2019
(GAP) List([0..10]. n-> (2*n+1)*239^(2*n+1)); # G. C. Greubel, Aug 26 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jun 30 2002
STATUS
approved