A212296 a(n) = numerator(1 + Sum_{k=1..n} n^2 / Product_{j=1..k} 4*j^2).

5, 33, 869, 48449, 1504375, 124787549, 119224713221, 10003972882859, 9610660732622149, 3811875515172994001, 40741092389313992153, 1050927826884051298685761, 707754011714996709527574437, 184405400463251288725766546203, 496687160874729261988243149308101

Offset

1,1

Links

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

Example

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

Maple

a := n -> numer(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_] := Numerator[G[n]]; Array[a, 15] (* Jean-François Alcover, Sep 05 2015, translated from PARI *)

Prog

(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)=numerator(G(n))
vector(15, n, a(n))

Crossrefs

Denominators are A212297.

Sequence in context: A295090 A350876 A268296 * A276160 A145505 A276126

Adjacent sequences: A212293 A212294 A212295 * A212297 A212298 A212299

Keyword

nonn,frac

Author

Charles R Greathouse IV, Jul 02 2012

Extensions

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

Status

approved