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A160259
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Numerator of Hermite(n, 11/29).
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1
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1, 22, -1198, -100364, 3837100, 759665192, -15557376776, -8008803406736, 6978879212432, 107919993983713120, 2268593594123893024, -1765305239735329031872, -80810233952657507431232, 33853095811859416015817344, 2511764683469716209839300480
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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) = 29^n * Hermite(n, 11/29).
E.g.f.: exp(22*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(22/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 22/29, -1198/841, -100364/24389, 3837100/707281,...
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MATHEMATICA
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Table[29^n*HermiteH[n, 11/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)
HermiteH[Range[0, 20], 11/29]//Numerator (* Harvey P. Dale, Mar 18 2023 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(exp(22*x - 841*x^2))) \\ G. C. Greubel, Sep 26 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(22/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 26 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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