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Denominator of zeta({6}_n)/Pi^(6*n).
1

%I #36 Jun 01 2022 14:44:45

%S 1,945,212837625,64965492466875,432684797065192546875,

%T 1347828286825972065254765625,197885500589205605585596463448046875,

%U 18132629348577543860598956218936672646484375,3673787208165374996876652878250276546299488037109375

%N Denominator of zeta({6}_n)/Pi^(6*n).

%C ({6}_n) is standard notation for multiple zeta values. It represents (6, ..., 6) where the multiplicity of 6 is n.

%H J. M. Borwein, D. M. Bradley, and D. J. Broadhurst, <a href="https://arxiv.org/abs/hep-th/9611004">Evaluations of k-fold Euler/Zagier sums: a compendium of results for arbitrary k</a>, arXiv:hep-th/9611004, 1996.

%H Roudy El Haddad, <a href="https://arxiv.org/abs/2102.00821">Multiple Sums and Partition Identities</a>, arXiv:2102.00821 [math.CO], 2021.

%H Roudy El Haddad, <a href="https://doi.org/10.7546/nntdm.2022.28.2.200-233">A generalization of multiple zeta value. Part 2: Multiple sums</a>. Notes on Number Theory and Discrete Mathematics, 28(2), 2022, 200-233, DOI: 10.7546/nntdm.2022.28.2.200-233.

%F a(n) = denominator(6*2^(6*n)/(6*n + 3)!).

%t a[n_] := Denominator[6*2^(6*n)/(6*n + 3)!]; Array[a, 9, 0] (* _Amiram Eldar_, Feb 19 2022 *)

%o (PARI) a(n) = denominator(6*2^(6*n)/(6*n + 3)!); \\ _Michel Marcus_, Feb 22 2022

%Y Cf. A351864 (numerators).

%Y Cf. A002432 (denominators of zeta(2*n)/Pi^(2*n)).

%Y Cf. A013664 (zeta(6)).

%Y Cf. A103345.

%K nonn,frac

%O 0,2

%A _Roudy El Haddad_, Feb 19 2022