A351806 Denominator of zeta({6}_n)/Pi^(6*n).

1, 945, 212837625, 64965492466875, 432684797065192546875, 1347828286825972065254765625, 197885500589205605585596463448046875, 18132629348577543860598956218936672646484375, 3673787208165374996876652878250276546299488037109375

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..8.

J. M. Borwein, D. M. Bradley, and D. J. Broadhurst, Evaluations of k-fold Euler/Zagier sums: a compendium of results for arbitrary k, arXiv:hep-th/9611004, 1996.

Roudy El Haddad, Multiple Sums and Partition Identities, arXiv:2102.00821 [math.CO], 2021.

Roudy El Haddad, A generalization of multiple zeta value. Part 2: Multiple sums. Notes on Number Theory and Discrete Mathematics, 28(2), 2022, 200-233, DOI: 10.7546/nntdm.2022.28.2.200-233.

Formula

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

Mathematica

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

Prog

(PARI) a(n) = denominator(6*2^(6*n)/(6*n + 3)!); \\ Michel Marcus, Feb 22 2022

Crossrefs

Cf. A351864 (numerators).

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

Cf. A013664 (zeta(6)).

Cf. A103345.

Sequence in context: A263889 A133353 A322252 * A119240 A257722 A093247

Adjacent sequences: A351803 A351804 A351805 * A351807 A351808 A351809

Keyword

nonn,frac

Author

Roudy El Haddad, Feb 19 2022

Status

approved