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A160148
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Numerator of Hermite(n, 20/27).
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1
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1, 40, 142, -110960, -5059508, 444738400, 54673349320, -1703637550400, -626141705175920, -5174439819171200, 8009253862551574240, 395813487065579065600, -112619873964978985037120, -11429947728298530733222400, 1677399182000270453064676480
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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, 20/27).
E.g.f.: exp(40*x - 729*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(40/27)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 40/27, 142/729, -110960/19683, -5059508/531441, ...
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MATHEMATICA
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Table[27^n*HermiteH[n, 20/27], {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(40*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(40/27)^(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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