A186414 a(n) = binomial(2n,n)^3/(n+1)^2.

1, 2, 24, 500, 13720, 444528, 16099776, 631628712, 26317863000, 1149330319280, 52120705189696, 2437827529099872, 117006104720150464, 5740095404246000000, 286939169121965760000, 14579498741074214418000

Offset: 0

Author

Emanuele Munarini, Feb 21 2011

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..559

Crossrefs

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

Programs

Magma

[Binomial(2*n,n)^3/(n+1)^2: n in [0..50]]; // Vincenzo Librandi, Mar 27 2011

Mathematica

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

Maxima

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

Formula

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