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Numerator of Hermite(n, 5/13).
1

%I #12 Sep 08 2022 08:45:43

%S 1,10,-238,-9140,149932,13856600,-114819080,-29249375600,-20831812720,

%T 78881993495200,852190309246240,-258099234921313600,

%U -5749435918990656320,989356137650941398400,35156582804554357854080,-4330067415318711118688000,-221544548972277705507065600

%N Numerator of Hermite(n, 5/13).

%H G. C. Greubel, <a href="/A159497/b159497.txt">Table of n, a(n) for n = 0..422</a>

%F From _G. C. Greubel_, Jun 12 2018: (Start)

%F a(n) = 13^n * Hermite(n,5/13).

%F E.g.f.: exp(10*x-169*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

%t Numerator[Table[HermiteH[n,5/13],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 14 2011 *)

%o (PARI) a(n)=numerator(polhermite(n,5/13)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(10/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 12 2018

%Y Cf. A159280, A159488.

%K sign,frac

%O 0,2

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