The Euler number En (resp. Entringer number E n,k) enumerates the alternating (down-up) permutations of {1,. .. , n} (resp. starting with k). The Springer number Sn (resp. Arnold number S n,k) enumerates the type B alternating permutations (resp. starting with k). In this paper, using bijections we first derive the counterparts in André permutations and Simsun permutations for the Entringer numbers (E n,k), and then the counterparts in signed André permutations and type B increasing 1-2 trees for the Arnold numbers (S n,k).