This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A065344 #20 Dec 12 2024 11:09:58
%S A065344 2,6,0,10,0,28,48,0,0,88,0,0,140,120,0,0,0,0,0,0,0,0,0,0,468,0,0,580,
%T A065344 0,496,704,0,0,420,0,0,494,0,0,574,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A065344 0,0,0,0,2016,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4320,0,0,4648,0,0,4988,0,0
%N A065344 a(n) = binomial(2*n,n) mod ((n+1)*(n+2)).
%H A065344 Harry J. Smith, <a href="/A065344/b065344.txt">Table of n, a(n) for n = 1..1000</a>
%H A065344 C. Pomerance, <a href="https://math.dartmouth.edu/~carlp/catalan5.pdf">Divisors of the middle binomial coefficient</a>, Amer. Math. Monthly, 112 (2015), 636-644.
%t A065344 Table[Mod[Binomial[2 n, n], (n + 1) (n + 2)], {n, 100}] (* _Bruno Berselli_, Jan 06 2014 *)
%o A065344 (PARI) a(n) = { binomial(2*n, n) % ((n + 1)*(n + 2)) } \\ _Harry J. Smith_, Oct 17 2009
%Y A065344 Cf. A000108, A065345, A065346, A065347, A065348, A065349.
%K A065344 nonn
%O A065344 1,1
%A A065344 _Labos Elemer_, Oct 30 2001