A254157 a(n) = binomial(3*n,n)^n.

1, 3, 225, 592704, 60037250625, 244217432431215243, 40928832685064366701940736, 287432029715751041166252933120000000, 85609985515193235253656684862285741981771256961, 1091210761769150876962680951989752349788052377750396728515625

Offset: 0

Author

Vaclav Kotesovec, Jan 26 2015

Keywords

• nonn
• easy

Comments

Generally, for p > 1 is

binomial(p*n,n) ~ (p^p/(p-1)^(p-1))^n * sqrt(p/(2*Pi*n*(p-1))) * (1 - (p^2-p+1)/(12*n*p*(p-1))).

binomial(p*n,n)^n ~ exp(-(p^2-p+1)/(12*p*(p-1))) * (p^p/(p-1)^(p-1))^(n^2) * (p/(2*Pi*n*(p-1)))^(n/2).

Crossrefs

Cf. A005809, A224733.

Programs

Mathematica

Table[Binomial[3n,n]^n,{n,0,10}]

Formula

a(n) ~ exp(-7/72) * 3^(3*n^2 + n/2) / (2^(2*n^2 + n) * Pi^(n/2) * n^(n/2)).