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%I #47 May 17 2020 11:15:00
%S 1,15,7875,11174163,209844223875,2475721174255329,
%T 123460585419481594375,5779795241720954566935675,
%U 3729407645972755442722659595875,485491404557154927712860942825333525,193817991848984690019014855170410665878125,56920344781273501874745734859262004352327035925
%N a(n) = denominator (2^(4*n-1) * (2^(4*n-2) - 1) * (Bernoulli(4*n-2) / (4*n-2)!) * ((2*n-2)! / Euler(2*n-2))^2 ).
%C See A334912.
%H X. Gourdon and P. Sebah, <a href="http://numbers.computation.free.fr/Constants/Miscellaneous/constantsNumTheory.html">Some Constants from Number theory</a>
%F a(n) = denominator (Product_{p = A065091, m_p = (p mod 4) - 2} ((p^(2*n - 1) + 1) / (p^(2*n - 1) - 1))^m_p) = denominator (2^(4*n) - 4) * ((2*n - 2)! / EulerE(2*n - 2))^2 * (zeta(4*n - 2) / Pi^(4*n - 2)).
%F a(n) = denominator((1 - 1/2^(4*n-2)) * zeta(4*n-2) / DirichletBeta(2*n-1)^2). - _Vaclav Kotesovec_, May 17 2020
%t Denominator[Table[2^(4*s - 1) * (2^(4*s - 2) - 1) * BernoulliB[4*s - 2] * (2*s - 2)!^2 / (EulerE[2*s - 2]^2 * (4*s - 2)!), {s, 1, 15}]] (* or *) Denominator[Table[(1 - 1/2^(4*s - 2))*Zeta[4*s - 2]/DirichletBeta[2*s - 1]^2, {s, 1, 15}]] (* _Vaclav Kotesovec_, May 17 2020 *)
%o (PARI) E(n) = subst(bernpol(2*n+1), 'x, 1/4)*4^(2*n+1)*(-1)^(n+1)/(2*n+1); \\ see A000364
%o a(n) = denominator((2^(4*n-1)*(2^(4*n-2)-1)*(bernfrac(4*n-2)/(4*n-2)!)*((2*n-2)!/ E(n-1))^2)); \\ _Michel Marcus_, May 17 2020
%Y Cf. A000040, A065091, A334912 (numerators).
%Y Cf. A000364, A027641/A027642.
%K nonn,frac
%O 1,2
%A _Dimitris Valianatos_, May 16 2020
%E More terms from _Michel Marcus_, May 17 2020
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