Copson-de Bruijn constant

The de Bruijn constant, also called the Copson-de Bruijn constant, is the minimal constant c = 1.1065... (OEIS A113276) such that the inequality sum_(n = 1)^∞ a_n<=c sum_(n = 1)^∞ sqrt((a_n^2 + a_(n + 1)^2 + a_(n + 2)^2 + ...)/n) always holds.