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A160184
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Numerator of Hermite(n, 1/28).
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1
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1, 1, -391, -1175, 458641, 2301041, -896635319, -6308683751, 2454058631585, 22238090874721, -8635680761357159, -95808996990263479, 37141246445981806129, 487826768288181211345, -188783965120435102822039, -2865977269485973590683399, 1107183737638672431002905921
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = 14^n * Hermite(n, 1/28).
E.g.f.: exp(x - 196*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/14)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 1/14, -391/196, -1175/2744, 458641/38416, ...
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MATHEMATICA
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Table[14^n*HermiteH[n, 1/28], {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(x - 196*x^2))) \\ G. C. Greubel, Sep 24 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(1/14)^(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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