%I #21 May 19 2022 10:53:11

%S 1,31,12307,1180906852403,4726403852635437852230311,

%T 26387151472737581442533784610190235872453672267436617,

%U 16379090991119093215568426722482532968867795792384100101494022155108529793899838205018451949281878220687877

%N Numerator of b(n) = n * Sum_{k=2^n..2^(n+1)-1} (-1)^k/k.

%H Amiram Eldar, <a href="/A073099/b073099.txt">Table of n, a(n) for n = 1..10</a>

%H 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 Sum_{k>=1} b(k) = gamma = 0.5772... (A001620).

%e The fractions begin with 1/6, 31/210, 12307/120120, 1180906852403/18050444111700, ...

%t a[n_] := Numerator[n * Sum[(-1)^k/k, {k, 2^n, 2^(n+1)-1}]]; Array[a, 7] (* _Amiram Eldar_, May 19 2022 *)

%o (PARI) a(n)=numerator( n*sum(k=2^n,2^(n+1)-1,(-1)^k/k))

%Y Cf. A001620, A073100 (denominators).

%K easy,frac,nonn

%O 1,2

%A _Benoit Cloitre_, Aug 18 2002