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A160104
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Numerator of Hermite(n, 5/27).
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2
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1, 10, -1358, -42740, 5512492, 304384600, -37142220680, -3034178687600, 348731717384080, 38877977386007200, -4187277821653825760, -608713688504523233600, 61068424818638825202880, 11260738942261526747094400, -1044883534589865025424443520
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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) = 27^n * Hermite(n, 5/27).
E.g.f.: exp(10*x - 729*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/27)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 10/27, -1358/729, -42740/19683, 5512492/531441..
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MATHEMATICA
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Numerator[Table[HermiteH[n, 5/27], {n, 0, 30}]] (* or *) Table[27^n* HermiteH[n, 5/27], {n, 0, 30}] (* G. C. Greubel, Jul 12 2018 *)
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PROG
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(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(10/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 12 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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