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a(n) = binomial(2n,n)^3/(n+1).
7

%I #17 Nov 01 2016 20:29:38

%S 1,4,72,2000,68600,2667168,112698432,5053029696,236860767000,

%T 11493303192800,573327757086656,29253930349198464,1521079361361956032,

%U 80361335659444000000,4304087536829486400000,233271979857187430688000,12774642558686527109607000,706008965215713532853436000,39337406606398593529683000000

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

%H Seiichi Manyama, <a href="/A186415/b186415.txt">Table of n, a(n) for n = 0..557</a>

%F G.f.: 3F2(1/2,1/2,1/2;1,2;64x), where 3F2(.,.,.;.,.;.) is a generalized hypergeometric series.

%F a(n) = A000888(n)*A000984(n). - _R. J. Mathar_, Feb 23 2011

%F a(n) ~ 64^n/(Pi^(3/2)*n^(5/2)). - _Ilya Gutkovskiy_, Nov 01 2016

%p A186415 := proc(n) binomial(2*n,n)^3/(n+1) ; end proc: # _R. J. Mathar_, Feb 23 2011

%t Table[Binomial[2n,n]^3/(n+1),{n,0,40}]

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

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

%K nonn,easy

%O 0,2

%A _Emanuele Munarini_, Feb 21 2011