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A122216
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Numerators in infinite products for Pi/2, e and e^gamma (unreduced).
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6
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1, 2, 4, 32, 4096, 201326592, 3283124128353091584, 26520146032764463901929624736590416838656, 840987221884558487834659180201583257033385988411167452990072842049923846092011283152896
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Product_{k=1..ceiling(n/2)} (2k)^binomial(n,2k-1).
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EXAMPLE
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Pi/2 = (2/1)^(1/2) * (4/3)^(1/4) * (32/27)^(1/8) * (4096/3645)^(1/16) * ...,
e = (2/1)^(1/1) * (4/3)^(1/2) * (32/27)^(1/3) * (4096/3645)^(1/4) * ... and
e^gamma = (2/1)^(1/2) * (4/3)^(1/3) * (32/27)^(1/4) * (4096/3645)^(1/5) * ....
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MATHEMATICA
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a[n_] := Product[(2k)^Binomial[n, 2k-1], {k, 1, n/2 // Ceiling}];
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CROSSREFS
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KEYWORD
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frac,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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