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A160300
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Numerator of Hermite(n, 2/31).
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1
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1, 4, -1906, -23000, 10897996, 220415984, -103848077624, -2957229437984, 1385343118601360, 51011732312847424, -23759618336314935584, -1075483968398187231616, 498023914992777619190464, 26797057907106900786753280, -12336437308381113989945920384
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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, 2/31).
E.g.f.: exp(4*x - 961*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/31)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 4/31, -1906/961, -23000/29791, 10897996/923521, ...
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MATHEMATICA
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Table[31^n*HermiteH[n, 2/31], {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(4*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018
(Maxima) makelist(num(hermite(n, 2/31)), n, 0, 20); /* Bruno Berselli, Mar 28 2018 */
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(4/31)^(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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