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A160303
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Numerator of Hermite(n, 5/31).
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1
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1, 10, -1822, -56660, 9939052, 534992600, -90164363720, -7071178300400, 1142359566484880, 120150033211799200, -18559035448937462240, -2494873992820155246400, 367426387533234274214080, 61216037645736403345110400, -8568355342448027542061898880
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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, 5/31).
E.g.f.: exp(10*x - 961*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/31)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 10/31, -1822/961, -56660/29791, 9939052/923521, ...
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MATHEMATICA
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Numerator/@HermiteH[Range[0, 20], 5/31] (* Harvey P. Dale, May 14 2011 *)
Table[31^n*HermiteH[n, 5/31], {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(10*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018
(Maxima) makelist(num(hermite(n, 5/31)), n, 0, 20); /* Bruno Berselli, Mar 28 2018 */
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(10/31)^(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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