Numbers in the base e^π

A large-scale experiment was conducted to find formulas relating to the base e^π. The numbers in this base are x = ∑ₙ₌₀^∞ a(n) eπn where $a(n)$ is taken from the OEIS catalog. These experiments were inspired by several facts. Indeed, it is known that the formula generating the partitions of integers is generated by an infinite product ∏k≥1^∞ 1 1-xᵏ = ∑ₙ₌₀^∞ p(n)xⁿ that when evaluated at x=e-π is equal to 23/8 Γ(3/4) π1/4 eπ/24\ . (1) By analyzing the 387500 sequences of the OEIS catalog, the model that was used is based on the fact that the infinite sum evaluated at e^π, is an expression that can be detected using a program like lindep from Pari-Gp. The process made it possible to find 793 expresssions similar to (1).