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%I #21 Dec 12 2024 11:09:54
%S 2,6,20,70,252,924,3432,990,14300,16588,17472,39676,4760,18360,46512,
%T 29070,30780,87780,0,191268,273240,322920,140400,58500,190008,350784,
%U 402752,611320,81840,649264,41888,164934,264180,295260,1316016,694564
%N a(n) = binomial(2*n, n) mod ((n+1)*(n+2)*(n+3)*(n+4)).
%H Harry J. Smith, <a href="/A065346/b065346.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 + 4))], {n, 100}] (* _Bruno Berselli_, Jan 06 2014 *)
%o (PARI) a(n) = { binomial(2*n, n) % ((n + 1)*(n + 2)*(n + 3)*(n + 4)) } \\ _Harry J. Smith_, Oct 17 2009
%Y Cf. A000108, A065344, A065345, A065347, A065348, A065349.
%K nonn
%O 1,1
%A _Labos Elemer_, Oct 30 2001