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A069071
a(n) = (2n+1) * ((2n+1)^4 + 4).
1
5, 255, 3145, 16835, 59085, 161095, 371345, 759435, 1419925, 2476175, 4084185, 6436435, 9765725, 14349015, 20511265, 28629275, 39135525, 52522015, 69344105, 90224355, 115856365, 147008615, 184528305, 229345195, 282475445, 345025455, 418195705, 503284595, 601692285
OFFSET
0,1
COMMENTS
The formula for Pi in the formula section was discovered by the mathematician and astronomer Nilakantha Somayaji (1444-1544) (Roy, 1990). - Amiram Eldar, Jan 18 2023
LINKS
Ranjan Roy, The Discovery of the Series Formula for Pi, Mathematics Magazine, Vol. 63, No. 5 (1990), pp. 291-306.
FORMULA
Pi = 16 * Sum_{n>=0} (-1)^n/a(n).
MATHEMATICA
a[n_] := (2*n + 1)*((2*n + 1)^4 + 4); Array[a, 30, 0] (* Amiram Eldar, Jul 16 2022 *)
CROSSREFS
Cf. A019683.
Sequence in context: A332125 A308652 A002770 * A275930 A181397 A283039
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Apr 05 2002
STATUS
approved