Une interprétation combinatoire des coefficients des développements en série entière des fonctions elliptiques de Jacobi

We give the first combinatorial interpretation of the coefficients of the power series of the elliptic Jacobi functions sn, cn and dn. This is done by introducing a new class of permutations enumerated by the Euler numbers and a new index about permutations having the same distribution as the Eulerian numbers.