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A064352
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a(n) = (3*n)!/(2*n)!.
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3
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1, 3, 30, 504, 11880, 360360, 13366080, 586051200, 29654190720, 1700755056000, 109027350432000, 7725366544896000, 599555620984320000, 50578512186237235200, 4608264443634948096000, 450974292794344230912000
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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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Integral representation as n-th moment of a positive function on a positive half-axis: a(n) = Integral_{x>=0} (x^n*exp(-2*x/27)*(BesselK(1/3, 2*x/27) + BesselK(2/3, 2*x/27))*(sqrt(3)/(27*Pi))).
From Carleman's criterion Sum_{n>=1} a(n)^(-1/(2*n) = infinity the above solution of the Stieltjes moment problem is unique. - Karol A. Penson, Jan 13 2018
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MATHEMATICA
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PROG
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(PARI) { f3=f2=1; for (n=0, 100, if (n, f3*=3*n*(3*n - 1)*(3*n - 2); f2*=2*n*(2*n - 1)); write("b064352.txt", n, " ", f3/f2) ) } \\ Harry J. Smith, Sep 12 2009
(Sage)
[falling_factorial(3*n, n) for n in (0..15)] # Peter Luschny, Jan 13 2018
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CROSSREFS
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KEYWORD
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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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