cp's OEIS Frontend

A334451 Decimal expansion of Product_{k>=1} (1 + 1/A002145(k)^5).

%I A334451 #17 Jun 27 2020 11:51:22
%S A334451 1,0,0,4,1,8,1,8,1,6,7,7,0,8,5,6,6,9,0,3,8,8,7,2,6,9,7,6,5,6,5,8,5,6,
%T A334451 9,6,0,6,3,1,5,8,1,9,5,0,6,3,6,7,4,3,2,8,8,2,8,3,4,2,4,9,7,6,8,6,9,7,
%U A334451 7,9,4,4,9,6,4,3,9,9,3,8,0,8,1,9,9,2,1,4,5,9,3,8,0,5,7,9,0,0,6,2,3,4,5,2,5
%N A334451 Decimal expansion of Product_{k>=1} (1 + 1/A002145(k)^5).
%C A334451 In general, for s>0, Product_{k>=1} (1 + 1/A002145(k)^(2*s+1))/(1 - 1/A002145(k)^(2*s+1)) = (2*s)! * (2^(2*s + 2) - 2) * zeta(2*s+1) / (Pi^(2*s+1) * A000364(s)). - _Dimitris Valianatos_, May 01 2020
%C A334451 In general, for s>1, Product_{k>=1} (1 + 1/A002145(k)^s)/(1 - 1/A002145(k)^s) = 2^s * (2^s - 1) * zeta(s) / (zeta(s, 1/4) - zeta(s, 3/4)).
%D A334451 B. C. Berndt, Ramanujan's notebook part IV, Springer-Verlag, 1994, p. 64-65.
%H A334451 Ph. Flajolet and I. Vardi, <a href="http://algo.inria.fr/flajolet/Publications/landau.ps">Zeta function expansions of some classical constants</a>, Feb 18 1996, p. 7-8.
%F A334451 A334451 / A334452 = 1488*zeta(5)/(5*Pi^5).
%F A334451 A334449 * A334451 = 90720*zeta(5)/Pi^10.
%e A334451 1.0041818167708566903887269765658569606315819506367432882834249768697794496439...
%Y A334451 Cf. A002145, A243381, A334426, A334447.
%K A334451 nonn,cons
%O A334451 1,4
%A A334451 _Vaclav Kotesovec_, Apr 30 2020
%E A334451 More digits from _Vaclav Kotesovec_, Jun 27 2020