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A160297
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Numerator of Hermite(n, 23/30).
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1
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1, 23, 79, -18883, -540959, 21547343, 1712746639, -18784653403, -5827198941119, -66400823394937, 22072936773448399, 806481251066529677, -90711968254039392479, -6441374025602166282817, 382513411697280621497359, 49378464830331101876186357
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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) = 15^n * Hermite(n, 23/30).
E.g.f.: exp(23*x - 225*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(23/15)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 23/15, 79/225, -18883/3375, -540959/50625, ...
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MATHEMATICA
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Numerator[HermiteH[Range[0, 20], 23/30]] (* Harvey P. Dale, Sep 30 2012 *)
Table[15^n*HermiteH[n, 23/30], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(exp(23*x - 225*x^2))) \\ G. C. Greubel, Oct 03 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(23/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 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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