%I A053991
%S A053991 3,4,6,5,17,8
%N A053991 Number of distinct residues of generalized Catalan number 1/((n^2-1)k+1){{n^2 
               k} choose k} modulo {n^2} as k runs through natural numbers.
%D A053991 F. Luca, P. Stanica, "Products of factorials modulo p", manuscript 2001.
%H A053991 P. Stanica, <a href="http://sciences.aum.edu/~stanpan/projects.htm">On 
               powerfree p^q-Catalan numbers</a>
%H A053991 P. Stanica, <a href="http://arXiv.org/abs/math.NT/0010148">p^q Catalan 
               numbers and squarefree binomial coefficients</a>
%F A053991 For p prime, p != 5, a(p) = p+1.
%F A053991 {1/((n^2-1)k+1){{n^2 k} choose {k}} modulo {n^2} | k\in N}
%e A053991 a(2)=3 since there are 3 residues of 1/((2^2-1)n+1){{2^2 n} choose {n}} 
               modulo {2^2}, namely {0,1,2}.
%Y A053991 Sequence in context: A057757 A058838 A001177 this_sequence A033957 A031131 
               A105321
%Y A053991 Adjacent sequences: A053988 A053989 A053990 this_sequence A053992 A053993 
               A053994
%K A053991 nonn,more
%O A053991 2,1
%A A053991 Pantelimon Stanica (pstanica(AT)mail.aum.edu), Apr 04 2000; corrected 
               Feb 08 2001.