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A160075
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Numerator of Hermite(n, 15/26).
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1
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1, 15, -113, -11835, -62943, 15056775, 332225295, -25551760275, -1169321452095, 51552138002175, 4330357927305615, -109290857537767275, -17739633636788785695, 177189213621352281975, 80605788404370208573455, 370627467209314130296125, -403111935202017245512974975
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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, 15/26).
E.g.f.: exp(15*x - 169*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(15/13)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 15/13, -113/169, -11835/2197, -62943/28561
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MATHEMATICA
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Numerator[HermiteH[Range[0, 20], 15/26]] (* Harvey P. Dale, Mar 13 2018 *)
Table[13^n*HermiteH[n, 15/26], {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(15*x - 169*x^2))) \\ G. C. Greubel, Sep 23 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(15/13)^(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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