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 A065345 #23 Dec 12 2024 11:09:46
%S A065345 2,6,20,70,252,420,552,0,1100,1144,0,1456,1400,2040,2448,0,3420,0,0,0,
%T A065345 6072,5520,0,5850,13104,0,12992,17980,22320,27280,5984,7854,7140,
%U A065345 15540,0,36556,13832,0,45920,24682,0,0,0,0,51888,0,23520,0,0,0,0,94446,0,0,0
%N A065345 a(n) = binomial(2*n,n) mod ((n+1)*(n+2)*(n+3)).
%H A065345 Harry J. Smith, <a href="/A065345/b065345.txt">Table of n, a(n) for n = 1..1000</a>
%H A065345 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 A065345 Table[Mod[Binomial[2 n, n], (n + 1) (n + 2) (n + 3)], {n, 60}] (* _Harvey P. Dale_, Feb 21 2012 *)
%o A065345 (PARI) a(n) = { binomial(2*n, n) % ((n + 1)*(n + 2)*(n + 3)) } \\ _Harry J. Smith_, Oct 17 2009
%Y A065345 Cf. A000108, A065344, A065346, A065347, A065348, A065349.
%K A065345 nonn
%O A065345 1,1
%A A065345 _Labos Elemer_, Oct 30 2001