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A212297
a(n) = denominator(1 + Sum_{k=1..n} n^2 / Product_{j=1..k} 4*j^2).
3
4, 16, 256, 9216, 196608, 11796480, 8493465600, 554906419200, 426168129945600, 138078474102374400, 1227364214243328000, 26731992586219683840000, 15397627729662537891840000, 3469598781750625204961280000, 8160496334677470482068930560000
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) = 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)
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 *)
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)=denominator(G(n))
vector(15, n, a(n))
CROSSREFS
Numerators are A212296.
Sequence in context: A139288 A152921 A215116 * A152153 A144988 A067172
KEYWORD
nonn,frac
AUTHOR
EXTENSIONS
Redefinition according to the data by Peter Luschny, Sep 26 2019
STATUS
approved