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Numerator of Hermite(n, 27/29).
1

%I #16 Sep 08 2022 08:45:45

%S 1,54,1234,-115020,-12437844,102210984,110121661176,4915056452976,

%T -1031159390225520,-121819606703423136,9031432087249072416,

%U 2536703117463027057984,-30117588135278876709696,-52827165482178797480672640,-2194115753871647145822109824

%N Numerator of Hermite(n, 27/29).

%H G. C. Greubel, <a href="/A160289/b160289.txt">Table of n, a(n) for n = 0..372</a>

%F From _G. C. Greubel_, Oct 03 2018: (Start)

%F a(n) = 29^n * Hermite(n, 27/29).

%F E.g.f.: exp(54*x - 841*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(54/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 54/29, 1234/841, -115020/24389, -12437844/707281, ...

%t Numerator[HermiteH[Range[0,20],27/29]] (* _Harvey P. Dale_, Sep 02 2011 *)

%t Table[29^n*HermiteH[n, 27/29], {n, 0, 30}] (* _G. C. Greubel_, Oct 03 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 27/29)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(54*x - 841*x^2))) \\ _G. C. Greubel_, Oct 03 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(54/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Oct 03 2018

%Y Cf. A009973 (denominators).

%K sign,frac

%O 0,2

%A _N. J. A. Sloane_, Nov 12 2009