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A059288 a(n) = binomial(2*n,n) mod n.

%I A059288 #32 Jul 22 2025 01:17:08
%S A059288 0,0,2,2,2,0,2,6,2,6,2,4,2,6,0,6,2,6,2,0,6,6,2,12,2,6,20,0,2,4,2,6,9,
%T A059288 6,7,16,2,6,20,20,2,0,2,4,0,6,2,12,2,6,3,44,2,6,32,32,39,6,2,36,2,6,
%U A059288 12,6,5,0,2,36,66,40,2,36,2,6,45,32,0,66,2,20,20,6,2
%N A059288 a(n) = binomial(2*n,n) mod n.
%H A059288 Chai Wah Wu, <a href="/A059288/b059288.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..5000 from T. D. Noe)
%F A059288 a(n) = Catalan(n) mod n. - _Jonathan Sondow_, Dec 13 2013
%F A059288 a(p) = 2, p an odd prime (provable using Wolstenholme's theorem). - _David Trimas_, Feb 11 2025
%p A059288 binomial(2*n,n) mod n;
%p A059288 seq(irem(binomial(2*n,n),n),n=1..83); # _Zerinvary Lajos_, Apr 20 2008
%t A059288 Table[Mod[Binomial[2*n, n], n], {n, 1, 25}] (* _G. C. Greubel_, Jan 04 2017 *)
%o A059288 (PARI) a(n) = binomial(2*n, n) % n; \\ _Harry J. Smith_, Jun 25 2009
%Y A059288 Cf. A014847, A053214, A059289, A000108.
%K A059288 nonn
%O A059288 1,3
%A A059288 _N. J. A. Sloane_, Jan 25 2001