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a(n) = binomial(2*n,n)^4/(n + 1)^2.
2

%I #14 Jan 13 2025 16:27:06

%S 1,4,144,10000,960400,112021056,14876193024,2167749739584,

%T 338710896810000,55880440123393600,9629613008027474176,

%U 1719721549507980904704,316402760115623198128384,59700436261400947600000000

%N a(n) = binomial(2*n,n)^4/(n + 1)^2.

%F G.f.: 4F3({1/2,1/2,1/2,1/2},{1,2,2},256x), where 4F3 is a hypergeometric series.

%t Table[Binomial[2n,n]^4/(n+1)^2,{n,0,40}]

%o (Maxima) makelist(binomial(2*n,n)^4/(n+1)^2,n,0,40);

%Y Cf. A000108, A002894, A000888, A002897, A186414, A186415, A186416.

%K easy,nonn

%O 0,2

%A _Emanuele Munarini_, Feb 21 2011