A224733 a(n) = binomial(2*n,n)^n.

1, 2, 36, 8000, 24010000, 1016255020032, 622345892187672576, 5608296349498479967469568, 752711194884611945703392100000000, 1518219588672387021538193329290752000000000, 46343145866349732399475841723454160331675252923826176

Offset: 0

Author

Paul D. Hanna, Apr 16 2013

Keywords

• nonn
• nice

Comments

a(n) = A000984(n)^n, where A000984 is the central binomial coefficients.

Examples

			L.g.f.: L(x) = 2*x + 36*x^2/2 + 8000*x^3/3 + 24010000*x^4/4 + 1016255020032*x^5/5 +...
Equivalently,
L(x) = 2*x + 6^2*x^2/2 + 20^3*x^3/3 + 70^4*x^4/4 + 252^5*x^5/5 + 924^6*x^6/6 + 3432^7*x^7/7 + 12870^8*x^8/8 +...+ A000984(n)^n*x^n/n +...
where exponentiation yields an integer series:
exp(L(x)) = 1 + 2*x + 20*x^2 + 2704*x^3 + 6008032*x^4 + 203263062688*x^5 + 103724721990326528*x^6 +...+ A224732(n)*x^n +...
		

Crossrefs

Cf. A224732, A000984.

Programs

Mathematica

Table[Binomial[2n,n]^n,{n,0,10}] (* Harvey P. Dale, Apr 19 2016 *)

PARI

{a(n)=binomial(2*n,n)^n}
for(n=0,20,print1(a(n),", "))

Formula

Logarithmic derivative of A224732 (when ignoring initial term a(0)=1).

a(n) ~ exp(-1/8) * 4^(n^2) / (n^(n/2) * Pi^(n/2)). - Vaclav Kotesovec, Mar 04 2014