A351864 Numerator of zeta({6}_n)/Pi^(6n).

1, 1, 4, 2, 4, 1, 4, 4, 4, 4, 16, 2, 4, 2, 8, 8, 4, 4, 16, 8, 16, 1, 4, 4, 4, 4, 16, 4, 8, 4, 16, 16, 4, 4, 16, 8, 16, 4, 16, 16, 16, 16, 64, 2, 4, 2, 8, 8, 4, 4, 16, 8, 16, 2, 8, 8, 8, 8, 32, 8, 16, 8, 32, 32, 4, 4, 16, 8, 16, 4, 16

Offset: 0

Author

Roudy El Haddad, Feb 22 2022

Keywords

• nonn
• easy
• frac

Comments

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

Links

• 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.

Crossrefs

Cf. A351806 (denominators).

Cf. A000120, A240883, A046988, A013664, A103345.

Programs

Mathematica

a[n_] := Numerator[6*2^(6*n)/(6*n + 3)!]; Array[a, 71, 0]

PARI

a(n) = 1 << (hammingweight(3*n+1) - 1);

Formula

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

a(n) = 2^(A000120(3*n + 1) - 1).

a(n) = 2^A240883(n).