The median Genocchi numbers, q-analogues and continued fractions

0. Introduction The Genocchi numbers appear in many different contexts (see e.g. [1,4,5,7,6,14,20]). Probably the most well-known definition uses the Seidel triangle 155 155 17 17 155 310 3 3 17 34 138 448 1 1 3 6 14 48 104 552 1 1 1 2 2 8 8 56 56 608 By definition, the triangle is formedby the numbers gk,n (k is the number of a row counted frombottom to top and n is the number of a column from left to right) with n = 1, 2, . . . and 1 ≤ k ≤ n+1 2 , subject to the relations g1,1 = 1 and gk,2n =  i≥k gi,2n−1, gk,2n+1 = 