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A160141
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Numerator of Hermite(n, 14/27).
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1
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1, 28, -674, -100520, 133516, 589971088, 15545858824, -4725783030752, -290982960018800, 46974010390164928, 5133550692291311584, -541141652104447925888, -97483852261892597109056, 6738266481886428192282880, 2036380397264732274988968064, -80522844304853268561187040768
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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, 14/27).
E.g.f.: exp(28*x - 729*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/27)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 28/27, -674/729, -100520/19683, 133516/531441, ...
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MATHEMATICA
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Table[27^n*HermiteH[n, 14/27], {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(28*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(28/27)^(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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