A184890 a(n) = C(2n,n) * (5^n/n!^2) * Product_{k=0..n-1} (5k+2)*(5k+3).

1, 60, 12600, 3640000, 1218262500, 443837394000, 170877396690000, 68390813462400000, 28171137810976875000, 11864338450927462500000, 5085530033605547526000000, 2211345876971860770960000000

Offset: 0

Author

Paul D. Hanna, Jan 25 2011

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 60*x + 12600*x^2 + 3640000*x^3 +...
A(x)^(1/2) = 1 + 30*x + 5850*x^2 + 1644500*x^3 +...+ A184889(n)*x^n +...
		

Crossrefs

Cf. A184889, A184892.

Programs

Mathematica

Table[Binomial[2*n, n] * 5^n / n!^2 * Product[(5*k + 2)*(5*k + 3), {k, 0, n - 1}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 07 2020 *)

PARI

{a(n)=(2*n)!/n!^2*(5^n/n!^2)*prod(k=0,n-1,(5*k+2)*(5*k+3))}

Formula

Self-convolution of A184889:

A184889(n) = (5^n/n!^2) * Product_{k=0..n-1} (10k+2)*(10k+3).

a(n) ~ sqrt(5 + sqrt(5)) * 2^(2*n - 3/2) * 5^(3*n) / (Pi^(3/2) * n^(3/2)). - Vaclav Kotesovec, Oct 07 2020