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A160147
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Numerator of Hermite(n, 19/27).
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1
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1, 38, -14, -111340, -4169684, 490886888, 49050698104, -2430351968272, -592964799643760, 5814962971461728, 8001852693840964384, 219288242242044652352, -120000760298623690001216, -8396695977614513457596800, 1955419963550761908894369664
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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) = 27^n * Hermite(n, 19/27).
E.g.f.: exp(38*x - 729*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(38/27)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 38/27, -14/729, -111340/19683, -4169684/531441, ...
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MATHEMATICA
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Table[27^n*HermiteH[n, 19/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(exp(38*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(38/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018
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CROSSREFS
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KEYWORD
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sign,frac
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AUTHOR
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STATUS
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approved
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