A212297 a(n) = denominator(1 + Sum_{k=1..n} n^2 / Product_{j=1..k} 4*j^2).

4, 16, 256, 9216, 196608, 11796480, 8493465600, 554906419200, 426168129945600, 138078474102374400, 1227364214243328000, 26731992586219683840000, 15397627729662537891840000, 3469598781750625204961280000, 8160496334677470482068930560000

Offset: 1

Author

Charles R Greathouse IV, Jul 02 2012

Keywords

• nonn
• frac

Examples

			r(n) = 5/4, 33/16, 869/256, 48449/9216, 1504375/196608, 124787549/11796480, ....
From _Petros Hadjicostas_, Sep 26 2019: (Start)
a(3) = denominator(1 + 3^2/(4*1^2) + 3^2/(4*1^2 * 4*2^2) + 3^2/(4*1^2 * 4*2^2 * 4*3^2)) = denominator(1 + 9/4 + 9/64 + 9/2304) = denominator(869/256) = 256.
a(4) = denominator(1 + 4^2/(4*1^2) + 4^2/(4*1^2 * 4*2^2) + 4^2/(4*1^2 * 4*2^2 * 4*3^2) + 4^2/(4*1^2 * 4*2^2 * 4*3^2 * 4*4^2)) = denominator(1 + 16/4 + 16/64 + 16/2304 + 16/147456) = denominator(48449/9216) = 9216.
(End)
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..225

Crossrefs

Numerators are A212296.

Programs

Maple

a := n -> denom(1 + add(n^2 / mul(4*j^2, j=1..k), k=1..n)):
seq(a(n), n=1..15); # Peter Luschny, Sep 26 2019

Mathematica

G[n_] := Module[{N=1, D=1}, Sum[N*=2*k-1; D*=2*k; (n/D)^2, {k, 1, n}] + 1]; a[n_] := Denominator[G[n]]; Array[a, 15] (* Jean-François Alcover, Sep 05 2015, translated from PARI *)

PARI

G(n)=my(N=1,D=1);sum(k=1,n,N*=2*k-1;D*=2*k;(n/D)^2)+1
a(n)=denominator(G(n))
vector(15, n, a(n))

Extensions

Redefinition according to the data by Peter Luschny, Sep 26 2019