A186414 - OEIS

%I #26 Sep 08 2022 08:45:55

%S 1,2,24,500,13720,444528,16099776,631628712,26317863000,1149330319280,

%T 52120705189696,2437827529099872,117006104720150464,

%U 5740095404246000000,286939169121965760000,14579498741074214418000

%N a(n) = binomial(2n,n)^3/(n+1)^2.

%H Seiichi Manyama, <a href="/A186414/b186414.txt">Table of n, a(n) for n = 0..559</a>

%F G.f.: 3F2({1/2, 1/2, 1/2}, {2, 2}, 64x), where 3F2 is a hypergeometric function.

%t Table[Binomial[2n, n]^3/(n + 1)^2, {n, 0, 20}]

%o (Maxima) makelist(binomial(2*n,n)^3/(n+1)^2,n,0,40);

%o (Magma) [Binomial(2*n,n)^3/(n+1)^2: n in [0..50]]; // _Vincenzo Librandi_, Mar 27 2011

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

%K nonn,easy

%O 0,2

%A _Emanuele Munarini_, Feb 21 2011