OFFSET
0,2
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.
FORMULA
sin(x)*sinh(x) = Sum_{n>=0} (-1)^n*x^(4n+2)/a(n). - Benoit Cloitre, Feb 02 2002
a(n) = Pi^(4n)/Zeta({4}_n) where ({4}_n) is the standard multiple zeta values notation for (4, ..., 4) where the multiplicity of 4 is n. - Roudy El Haddad, Feb 19 2022
From Amiram Eldar, Feb 25 2022: (Start)
Sum_{n>=0} 1/a(n) = (cosh(sqrt(2)) - cos(sqrt(2)))/2.
Sum_{n>=0} (-1)^n/a(n) = sin(1)*sinh(1). (End)
MATHEMATICA
Table[(4n+2)!/2^(2n+1), {n, 0, 10}] (* Amiram Eldar, Feb 25 2022 *)
PROG
(PARI) a(n) = (4*n+2)!/2^(2*n+1); \\ Michel Marcus, Feb 20 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 05 2000
STATUS
approved