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A067770 a(n) = Catalan(n) mod (n+2).

%I A067770 #25 Mar 06 2025 11:41:08
%S A067770 1,1,2,0,2,0,4,6,0,0,8,0,0,10,8,0,0,0,0,0,0,0,0,0,0,18,0,0,20,0,16,22,
%T A067770 0,0,12,0,0,13,0,0,14,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,32,0,
%U A067770 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,54,0,0,56,0,0,58,0,0
%N A067770 a(n) = Catalan(n) mod (n+2).
%H A067770 Alois P. Heinz, <a href="/A067770/b067770.txt">Table of n, a(n) for n = 0..10000</a>
%p A067770 a:= n-> binomial(2*n, n)/(n+1) mod (n+2):
%p A067770 seq(a(n), n=0..88);
%t A067770 Table[Mod[CatalanNumber[n],n+2],{n,0,90}] (* _Harvey P. Dale_, Mar 06 2025 *)
%o A067770 (PARI) for(k=0,80,print1(binomial(2*k,k)/(k+1)%(k+2),", ")) \\ _Hugo Pfoertner_, Jul 16 2020
%o A067770 (Python)
%o A067770 A067770_list, c = [1,1], 1
%o A067770 for n in range(2,10001):
%o A067770     c = c*(4*n-2)//(n+1)
%o A067770     A067770_list.append(c % (n+2)) # _Chai Wah Wu_, Jul 16 2020
%Y A067770 Cf. A000108, A059288.
%K A067770 nonn
%O A067770 0,3
%A A067770 Claude Lenormand (claude.lenormand(AT)free.fr), Feb 05 2002
%E A067770 Name corrected by _Hugo Pfoertner_, Jul 16 2020