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A160073
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Numerator of Hermite(n, 9/26).
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1
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1, 9, -257, -8397, 185025, 13017969, -195530529, -28160215893, 209183288577, 78027873371865, 65915296495551, -263140974328443741, -2613341841326452287, 1043779715304229742913, 20877041488526499035295, -4751272239422876652146661, -148608050501635239978265599
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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) = 13^n * Hermite(n, 9/26).
E.g.f.: exp(9*x - 169*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(9/13)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 9/13, -257/169, -8397/2197, 185025/28561
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MATHEMATICA
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Numerator[HermiteH[Range[0, 20], 9/26]] (* Harvey P. Dale, Jul 18 2015 *)
Table[13^n*HermiteH[n, 9/26], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(exp(9*x - 169*x^2))) \\ G. C. Greubel, Sep 23 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(9/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 23 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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