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A068205
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Denominator of S(n)/Pi^n, where S(n) = Sum((4k+1)^(-n),k,-inf,+inf).
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3
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4, 8, 32, 96, 1536, 960, 184320, 161280, 8257536, 2903040, 14863564800, 638668800, 1569592442880, 49816166400, 5713316492083200, 83691159552000, 1096956766479974400, 2845499424768000, 6713375410857443328000
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OFFSET
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1,1
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LINKS
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FORMULA
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There is a simple formula in terms of Euler and Bernoulli numbers.
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EXAMPLE
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The first few values of S(n)/Pi^n are 1/4, 1/8, 1/32, 1/96, 5/1536, 1/960, ...
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MATHEMATICA
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s[n_?EvenQ] := (-1)^(n/2-1)*(2^n-1)*BernoulliB[n]/(2*n!); s[n_?OddQ] := (-1)^((n-1)/2)*2^(-n-1)*EulerE[n-1]/(n-1)!; Table[s[n] // Denominator, {n, 1, 19}] (* Jean-François Alcover, May 13 2013 *)
a[n_] := Sum[((-1)^k/(2*k+1))^n, {k, 0, Infinity}] /. Pi -> 1 // Denominator; Table[a[n], {n, 1, 19}] (* Jean-François Alcover, Jun 20 2014 *)
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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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STATUS
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approved
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