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A160328
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Numerator of Hermite(n, 20/31).
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1
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1, 40, -322, -166640, -4808948, 1088770400, 89764806280, -8965108001600, -1566300023755120, 75195499682396800, 30101677798211937760, -241190391967188985600, -646057287688484347545920, -20279476307208127137958400, 15331208337896144822264021120
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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) = 31^n * Hermite(n, 20/31).
a(n+2) = 40*a(n+1) - 1922*(n+1)*a(n)
E.g.f.: exp(40*x - 961*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(40/31)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 40/31, -322/961, -166640/29791, -4808948/923521, ...
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MATHEMATICA
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Table[31^n*HermiteH[n, 20/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(exp(40*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(40/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 04 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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