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%I #10 May 09 2020 00:27:53
%S 1,1,5,7,47,37,319,533,1879,1627,20417,18107,263111,237371,261395,
%T 95549,1768477,1632341,33464927,155685007,166770367,156188887,
%U 3825136961,3602044091,19081066231,18051406831,57128792093,54260455193
%N Numerator of the product of n and the n-th alternating harmonic number, Sum_{k=1..n} (-1)^(k+1)/k.
%C a(n) almost always equals A058313(n), which is the numerator of the n-th alternating harmonic number, Sum ((-1)^(k+1)/k, k=1..n), except for n = 15, 28, 75, 77, 104, ... The ratio a(n)/A058313(n) for n = 1..400 is given in A119788.
%F a(n) = numerator(Sum_{k=1..n} (-1)^(k+1)*n/k).
%e The first few fractions are 1, 1, 5/2, 7/3, 47/12, 37/10, 319/60, 533/105, 1879/280, ... = A119787/A334721. - _Petros Hadjicostas_, May 08 2020
%t Numerator[Table[Sum[(-1)^(i+1)*n/i, {i, 1, n}],{n,1,50}]]
%o (PARI) a(n) = numerator(n*sum(k=1, n, (-1)^(k+1)/k)); \\ _Michel Marcus_, May 09 2020
%Y Cf. A058313, A119788, A334721 (denominators).
%K frac,nonn
%O 1,3
%A _Alexander Adamchuk_, Jun 26 2006
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