Some properties of a sequence analogous to Euler numbers

Let {U n } be given by U 0 = 1 and U n = −2 [n/2] k=1 n 2k U n−2k (n ≥ 1), where [·] is the greatest integer function. Then {U n } is an analogy of Euler numbers and U 2n = 3 2n E 2n (1 3), where E m (x) is the Euler polynomial. In a previous paper the author gave many properties of {U n }. In the paper we present a summation formula and several congruences involving {U n }.