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A073100 Denominator of b(n) = n * Sum_{k=2^n..2^(n+1)-1} (-1)^k/k.

%I A073100 #19 May 20 2022 08:56:20
%S A073100 6,210,120120,18050444111700,118226688410282226751136160,
%T A073100 1112813007583117631616979100370019711878239390670756000,
%U A073100 1191035057635417333689929196555456096447880322064975132139675263681349241137859495385119040334214863238544000
%N A073100 Denominator of b(n) = n * Sum_{k=2^n..2^(n+1)-1} (-1)^k/k.
%H A073100 Amiram Eldar, <a href="/A073100/b073100.txt">Table of n, a(n) for n = 1..10</a>
%H A073100 G. Vacca, <a href="https://books.google.fr/books?id=Q4qXAAAAMAAJ&amp;hl=fr&amp;pg=PA363#v=onepage&amp;q&amp;f=false">A new series for the Eulerian constant gamma=.577...</a>, Quart. J. Pure Appl. Math., Vol. 41 (1910), pp. 363-368.
%F A073100 Sum_{k>=1} b(k) = gamma = 0.5772... (A001620).
%t A073100 a[n_] := Denominator[n * Sum[(-1)^k/k, {k, 2^n, 2^(n+1)-1}]]; Array[a, 7] (* _Amiram Eldar_, May 19 2022 *)
%o A073100 (PARI) a(n)=denominator( n*sum(k=2^n,2^(n+1)-1,(-1)^k/k))
%Y A073100 Cf. A001620, A073099 (numerators).
%K A073100 easy,frac,nonn
%O A073100 1,1
%A A073100 _Benoit Cloitre_, Aug 18 2002