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A212297
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a(n) = denominator(1 + Sum_{k=1..n} n^2 / Product_{j=1..k} 4*j^2).
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3
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4, 16, 256, 9216, 196608, 11796480, 8493465600, 554906419200, 426168129945600, 138078474102374400, 1227364214243328000, 26731992586219683840000, 15397627729662537891840000, 3469598781750625204961280000, 8160496334677470482068930560000
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OFFSET
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1,1
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LINKS
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EXAMPLE
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r(n) = 5/4, 33/16, 869/256, 48449/9216, 1504375/196608, 124787549/11796480, ....
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)
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MAPLE
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a := n -> denom(1 + add(n^2 / mul(4*j^2, j=1..k), k=1..n)):
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MATHEMATICA
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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 *)
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PROG
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(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))
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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