On a conjecture of Deutsch, Sagan, and Wilson
  We prove a recent conjecture due to Deutsch, Sagan, and Wilson stating that the finite sequence obtained from the first p central trinomial coefficients modulo p by replacing nonzero terms by 1's is palindromic, for any prime number p > 3.   Addendum: the result was proved before almost in the same way by Tony D. Noe:   On the Divisibility of Generalized Central Trinomial Coefficients,   Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7 http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Noe/noe35.html 
Jean-Paul Allouche