A186415 a(n) = binomial(2n,n)^3/(n+1).

1, 4, 72, 2000, 68600, 2667168, 112698432, 5053029696, 236860767000, 11493303192800, 573327757086656, 29253930349198464, 1521079361361956032, 80361335659444000000, 4304087536829486400000, 233271979857187430688000, 12774642558686527109607000, 706008965215713532853436000, 39337406606398593529683000000

Offset: 0

Author

Emanuele Munarini, Feb 21 2011

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..557

Crossrefs

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

Programs

Maple

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

Mathematica

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

Maxima

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

Formula

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

a(n) = A000888(n)*A000984(n). - R. J. Mathar, Feb 23 2011

a(n) ~ 64^n/(Pi^(3/2)*n^(5/2)). - Ilya Gutkovskiy, Nov 01 2016