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%I #12 May 05 2022 07:17:39
%S 1,2,43,244,1483,42494,4421639,3975704,17273323,3917984134,
%T 46801334969,1002549557332,735057842971,13139661722338,
%U 2022120072706607,59425819929320912,1064450614009503859,3045237174301650742,2242901701823948775361,2149021201829850641044
%N Numerator of b(n) = Sum_{k=1..n} (-1)^(k+1)/k*Sum_{i=0..k-1} (-1)^i/(2*i+1).
%H Amiram Eldar, <a href="/A073594/b073594.txt">Table of n, a(n) for n = 1..772</a>
%F Limit_{n -> infinity} b(n) = G, the Catalan constant (A006752).
%t Numerator[Accumulate[Table[(-1)^(k + 1)/k * Sum[(-1)^i/(2*i + 1), {i, 0, k - 1}], {k, 1, 20}]]] (* _Amiram Eldar_, May 05 2022 *)
%o (PARI) a(n)=numerator( sum(k=1,n,(-1)^(k+1)/k*sum(i=0,k-1,(-1)^i/(2*i+1))))
%Y Cf. A006752, A073595 (denominators).
%K easy,frac,nonn
%O 1,2
%A _Benoit Cloitre_, Aug 28 2002
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