A185404 a(n) = C(2n,n) * (7^n/n!^2) * Product_{k=0..n-1} (7k+3)*(7k+4).

1, 168, 97020, 76969200, 70715452500, 70710926711040, 74713950839848320, 82063363963278297600, 92763657280052631873000, 107208829261440251585240000, 126104599836427618807641720480

Offset: 0

Author

Paul D. Hanna, Jan 26 2011

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 168*x + 97020*x^2 + 76969200*x^3 +...
A(x)^(1/2) = 1 + 84*x + 44982*x^2 + 34706112*x^3 +...+ A185403(n)*x^n +...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..320

Crossrefs

Cf. A184896, A185402, A185403.

Programs

Mathematica

Table[Binomial[2*n, n]*(7^n/(n!)^2)*Product[(7*k + 3)*(7*k + 4), {k, 0, n - 1}], {n, 0, 50}] (* G. C. Greubel, Jun 29 2017 *)

PARI

{a(n)=(2*n)!/n!^2*(7^n/n!^2)*prod(k=0,n-1,(7*k+3)*(7*k+4))}

Formula

Self-convolution of A185403:

A185403(n) = (7^n/n!^2) * Product_{k=0..n-1} (14k+3)*(14k+4).

a(n) ~ cos(Pi/14) * 2^(2*n) * 7^(3*n) / (Pi*n)^(3/2). - Vaclav Kotesovec, Oct 23 2020