OFFSET
0,2
COMMENTS
REFERENCES
E. Maor, Trigonometric Delights, Princeton University Press, 1998, p. 205.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
R. Ayoub, Euler and the Zeta Function, Am. Math. Monthly 81 (1974) 1067-1086, p. 1070.
W. Lang, Rationals and limit.
FORMULA
a(n) = numerator(r(n)) with the rationals (in lowest terms) r(n) = Sum_{k=0..n} (-1)^floor(k/2)/(2*k+1).
EXAMPLE
Rationals r(n): [1, 4/3, 17/15, 104/105, 347/315, 4132/3465, ...].
MATHEMATICA
Numerator[Table[Sum[(-1)^Floor[k/2]/(2*k + 1), {k, 0, n}], {n, 0, 50}]] (* G. C. Greubel, Aug 17 2018 *)
PROG
(PARI) a(n) = numerator(sum(k=0, n, (-1)^(k\2)/(2*k+1))); \\ Michel Marcus, Oct 03 2017
(Magma) [Numerator((&+[(-1)^Floor(k/2)/(1+2*k): k in [0..n]])): n in [0..50]]; // G. C. Greubel, Aug 17 2018
CROSSREFS
KEYWORD
nonn,easy,frac
AUTHOR
Wolfdieter Lang, Mar 07 2007
STATUS
approved