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A327495
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a(n) = numerator( Sum_{j=0..n} (j!/(2^j*floor(j/2)!)^2)^2 ).
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6
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1, 17, 69, 1113, 17817, 285297, 1141213, 18260633, 1168681737, 18699007017, 74796032037, 1196736992841, 19147791938817, 306364680039081, 1225458720340365, 19607339566855065, 5019478929156305865, 80311662878468159865, 321246651514020383485, 5139946424277661728785
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OFFSET
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0,2
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COMMENTS
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This sequence is a variant of the Landau constants when the normalized central binomial is replaced by the normalized swinging factorial.
(1) A277233(n)/4^A005187(n) are the Landau constants. These constants are defined as G(n) = Sum_{j=0..n} g(j)^2 with the normalized central binomial
(2) A327495(n)/4^A327492(n) are the rationals considered here. These numbers are defined as H(n) = Sum_{j=0..n} h(j)^2 with the normalized swinging factorial
(3) In particular, this means that we have the pure integer representations
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LINKS
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FORMULA
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EXAMPLE
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r(n) = 1, 17/16, 69/64, 1113/1024, 17817/16384, 285297/262144, 1141213/1048576, 18260633/16777216, ...
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MAPLE
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A327495 := n -> numer(add(j!^2/(2^j*iquo(j, 2)!)^4, j=0..n)):
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PROG
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(PARI) a(n)={ numerator(sum(j=0, n, (j!/(2^j*(j\2)!)^2)^2 )) } \\ Andrew Howroyd, Sep 28 2019
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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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STATUS
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approved
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