A184891 a(n) = (5^n/n!^2) * Product_{k=0..n-1} (10k+1)*(10k+4).

1, 20, 3850, 1078000, 355066250, 128107903000, 49001272897500, 19520507080800000, 8012558140822125000, 3365274419145292500000, 1439327869068441602250000, 624739666805574817770000000

Offset: 0

Author

Paul D. Hanna, Jan 25 2011

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 20*x + 3850*x^2 + 1078000*x^3  +...
A(x)^2 = 1 + 40*x + 8100*x^2 + 2310000*x^3  +...+ A184892(n)*x^n +...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A184892; variants: A184424, A178529, A092870, A184895, A184897.

Programs

Mathematica

Table[5^n/(n!)^2 Product[(10k+1)(10k+4),{k,0,n-1}],{n,0,20}] (* Harvey P. Dale, Feb 02 2012 *)
FullSimplify[Table[2^(2*n) * 5^(3*n) * Gamma[n+1/10] * Gamma[n+2/5] / (Gamma[2/5] * Gamma[1/10] * Gamma[n+1]^2), {n, 0, 15}]] (* Vaclav Kotesovec, Jul 03 2014 *)

PARI

{a(n)=(5^n/n!^2)*prod(k=0,n-1,(10*k+1)*(10*k+4))}

Formula

Self-convolution yields Sum_{k=0..n} a(n-k)*a(k) = A184892(n) where

. A184892(n) = C(2n,n) * (5^n/n!^2)*Product_{k=0..n-1} (5k+1)*(5k+4).