Some Identities and Congruences on ballot Numbers 

Author  ChenYing 
Tutor  GuoJunWei 
School  East China Normal University 
Course  Operational Research and Cybernetics 
Keywords  ballot number congruences modulo Catalan triangle identities Catalan number central binomial coefficient 
CLC  O157 
Type  Master's thesis 
Year  2013 
Downloads  5 
Quotes  0 
We first prove the following identity on ballot numbers conjectured by Miana and Romero:For m, n∈Z+, there holds where Cn=1/n+1(2n/n) is the nth Catalan number. Then we give a summation formula for the following generalized form by applying the Newton interpolation formula. For example, we prove thatWe also give congruences on sums and alternating sums of ballot numbers m (2k+m/k) modulo p. For example, for any prime p>3, we havewhile for any prime p>5, we have