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A160131
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Numerator of Hermite(n, 8/27).
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1
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1, 16, -1202, -65888, 4203340, 451512256, -23418152504, -4324519655552, 169813349966992, 53158210861830400, -1377759404477582624, -797090864837128553984, 9343051491617413259968, 14095390595056279792663552, 48438051548784025753183360, -286940104001508238715797489664
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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, 8/27).
E.g.f.: exp(16*x - 729*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/27)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 16/27, -1202/729, -65888/19683, 4203340/531441, ...
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MATHEMATICA
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Table[27^n*HermiteH[n, 8/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(exp(16*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(16/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 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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