Judsan Constants

I define a family of constants derived from trinomial coefficients, which I call Judsan's Constants: C_k = sumₙ₌₁∞ (kn)! / ((n!)^k · kᵏⁿ) · 1/(n(n+1)), k ≥ 2 For k = 3, this gives Judsan's Constant: C_3 ≈ 0.14775 I prove absolute convergence using Stirling's approximation, establish the exact value C_2 = 2 ln 2 - 1, and derive a single-variable hypergeometric integral representation for C_3. A literature search confirms that these constants have not previously appeared. This work introduces a new family of hypergeometric constants with open questions regarding closed forms and arithmetic properties.