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

6, 210, 120120, 18050444111700, 118226688410282226751136160, 1112813007583117631616979100370019711878239390670756000, 1191035057635417333689929196555456096447880322064975132139675263681349241137859495385119040334214863238544000

Offset: 1

Author

Benoit Cloitre, Aug 18 2002

Keywords

• easy
• frac
• nonn

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, A073099 (numerators).

Programs

Mathematica

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

PARI

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

Formula

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