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A160306
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Numerator of Hermite(n, 8/31).
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1
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1, 16, -1666, -88160, 8195596, 808903616, -65817219704, -10381352014976, 719403241658000, 171134120448798976, -9706091347019300384, -3444495256578225124864, 150094259153430446720704, 81845346744175071427394560, -2440729611300811998925197184
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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, 8/31).
E.g.f.: exp(16*x - 961*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/31)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 16/31, -1666/961, -88160/29791, 8195596/923521, ...
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MATHEMATICA
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Table[31^n*HermiteH[n, 8/31], {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(16*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018
(Maxima) makelist(num(hermite(n, 8/31)), n, 0, 20); /* Bruno Berselli, Mar 28 2018 */
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(16/31)^(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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