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A160140
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Numerator of Hermite(n, 13/27).
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1
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1, 26, -782, -96148, 920620, 584671256, 8490132856, -4893960693232, -213893273952368, 51521932403096480, 4146277783283481376, -643386552071776162624, -83226053442166654536512, 9092813725551462723320192, 1813879773807164800891373440
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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, 13/27).
E.g.f.: exp(26*x - 729*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/27)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 26/27, -782/729, -96148/19683, 920620/531441
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MATHEMATICA
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Table[27^n*HermiteH[n, 13/27], {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(26*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(26/27)^(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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