A186416 a(n) = binomial(2n,n)^4/(n+1)^3.

1, 2, 48, 2500, 192080, 18670176, 2125170432, 270968717448, 37634544090000, 5588044012339360, 875419364366134016, 143310129125665075392, 24338673855047938317568, 4264316875814353400000000, 767401591466550107174400000, 141345980472409642279275210000, 26569505644587874058090478570000

Offset: 0

Author

Emanuele Munarini, Feb 21 2011

Keywords

• easy
• nonn

Crossrefs

Cf. A000108, A002894, A000888, A002897, A186414, A186415.

Programs

Maple

A186416 := proc(n) binomial(2*n,n)^4/(n+1)^3 ; end proc: # R. J. Mathar, Feb 23 2011

Mathematica

Table[Binomial[2n,n]^4/(n+1)^3,{n,0,40}]

Maxima

makelist(binomial(2*n,n)^4/(n+1)^3,n,0,40);

Formula

G.f.: 4F3(1/2,1/2,1/2,1/2;2,2,2;256*x), where nFm(...;..;.) denotes a generalized hypergeometric series.

a(n) = (A000108(n))^3*A000984(n). - R. J. Mathar, Feb 23 2011