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A160065
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Numerator of Hermite(n, 21/25).
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1
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1, 42, 514, -83412, -5430804, 188966232, 41879106744, 341675743248, -352091802793584, -18204613149810528, 3196439029135777824, 361808103596334268608, -28755096299570905798464, -6634835598526992072655488, 188607219729893552173509504, 124031126202877890462758439168
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OFFSET
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0,2
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..380
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FORMULA
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From G. C. Greubel, Sep 23 2018: (Start)
a(n) = 25^n * Hermite(n, 21/25).
E.g.f.: exp(42*x - 625*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(42/25)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 42/25, 514/625, -83412/15625, -5430804/390625, ...
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MATHEMATICA
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Table[25^n*HermiteH[n, 21/25], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)
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PROG
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(PARI) a(n)=numerator(polhermite(n, 21/25)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(42*x - 625*x^2))) \\ G. C. Greubel, Sep 23 2018
(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(42/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 23 2018
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CROSSREFS
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Cf. A009969 (denominators).
Sequence in context: A263289 A273223 A163727 * A196671 A248448 A248449
Adjacent sequences: A160062 A160063 A160064 * A160066 A160067 A160068
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KEYWORD
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sign,frac
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AUTHOR
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N. J. A. Sloane, Nov 12 2009
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STATUS
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approved
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