A073099 Numerator of b(n) = n * Sum_{k=2^n..2^(n+1)-1} (-1)^k/k.

1, 31, 12307, 1180906852403, 4726403852635437852230311, 26387151472737581442533784610190235872453672267436617, 16379090991119093215568426722482532968867795792384100101494022155108529793899838205018451949281878220687877

Offset: 1

Author

Benoit Cloitre, Aug 18 2002

Keywords

• easy
• frac
• nonn

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10
• G. Vacca, A new series for the Eulerian constant gamma=.577..., Quart. J. Pure Appl. Math., Vol. 41 (1910), pp. 363-368.

Crossrefs

Cf. A001620, A073100 (denominators).

Programs

Mathematica

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

PARI

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

Formula

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