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%I #18 Sep 08 2022 08:45:29
%S 1,4,17,104,347,4132,50251,47248,848261,16882724,16189889,357817912,
%T 1856017421,5753962988,161845337077,4871637351712,5008383140437,
%U 5137314884092,185568039683479,181286844605704,7599727236867089
%N Numerators of partial sums of a series for Pi*sqrt(2)/4.
%C Denominators coincide with A025547(n+1) for n=0..41, but then start to differ. See the W. Lang link. denominator(r(42))=7422822568422519986207785205976075 but the corresponding entry is A025547(43)=126187983663182839765532348501593275.
%D E. Maor, Trigonometric Delights, Princeton University Press, 1998, p. 205.
%H G. C. Greubel, <a href="/A127676/b127676.txt">Table of n, a(n) for n = 0..1000</a>
%H R. Ayoub, <a href="http://www.jstor.org/stable/2319041">Euler and the Zeta Function</a>, Am. Math. Monthly 81 (1974) 1067-1086, p. 1070.
%H W. Lang, <a href="/A127676/a127676.txt">Rationals and limit. </a>
%F a(n) = numerator(r(n)) with the rationals (in lowest terms) r(n) = Sum_{k=0..n} (-1)^floor(k/2)/(2*k+1).
%e Rationals r(n): [1, 4/3, 17/15, 104/105, 347/315, 4132/3465, ...].
%t Numerator[Table[Sum[(-1)^Floor[k/2]/(2*k + 1), {k, 0, n}], {n, 0, 50}]] (* _G. C. Greubel_, Aug 17 2018 *)
%o (PARI) a(n) = numerator(sum(k=0, n, (-1)^(k\2)/(2*k+1))); \\ _Michel Marcus_, Oct 03 2017
%o (Magma) [Numerator((&+[(-1)^Floor(k/2)/(1+2*k): k in [0..n]])): n in [0..50]]; // _G. C. Greubel_, Aug 17 2018
%Y Cf. A025547 (denominators).
%K nonn,easy,frac
%O 0,2
%A _Wolfdieter Lang_, Mar 07 2007
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