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