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The first column is a(n)/b(n) = 1, 3/2, 19/6, 7, 449/30, 31, 2647/42, 127, 7649/30, 511, 67523/66, 2047, ... , , where the denominators are b(n) = A027642(n).
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G. C. Greubel, <a href="/A244605/b244605.txt">Table of n, a(n) for n = 0..500</a>
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(PARI) {a(n) = if( n<0, 0, 2*(n==1) + numerator( bernfrac(n) + 2^n - 1))}; /* Michael Somos, Aug 05 2014 */
reviewed
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a[n_] := BernoulliB[n]+2^n-1 // Numerator; a[1] = 3; Table[a[n], {n, 0, 32}] (* Jean-François Alcover, Jul 25 2014 *)
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