A184898 a(n) = C(2n,n) * (8^n/n!^2) * Product_{k=0..n-1} (8k+1)*(8k+7).

1, 112, 90720, 105100800, 142542960000, 211337613527040, 331831362513530880, 542307255307827609600, 912855634598629193472000, 1571864775032876891607040000, 2755743023914838714304931102720

Offset: 0

Author

Paul D. Hanna, Jan 25 2011

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 112*x + 90720*x^2 + 105100800*x^3 +...
A(x)^(1/2) = 1 + 56*x + 43792*x^2 + 50098048*x^3 +...+ A184897(n)*x^n +...
		

Crossrefs

Cf. A184897; variants: A184423, A008977, A184892, A001421, A184896.

Programs

PARI

{a(n)=(2*n)!/n!^2*(8^n/n!^2)*prod(k=0,n-1,(8*k+1)*(8*k+7))}

Formula

Self-convolution of A184897, where A184897(n) = (8^n/n!^2) * Product_{k=0..n-1} (16k+1)*(16k+7).

a(n) ~ sqrt(2-sqrt(2)) * 2^(11*n - 1) / (Pi^(3/2) * n^(3/2)). - Vaclav Kotesovec, Oct 05 2020