login
Numerator of Hermite(n, 12/13).
1

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

%S 1,24,238,-10512,-493620,2365344,890986056,16586747712,-1709991063408,

%T -85890351335040,3140424382846176,365679572700743424,

%U -2899788110604240192,-1552791261528717092352,-24525321318694178812800,6759200537905228989502464,286564191995504982328955136

%N Numerator of Hermite(n, 12/13).

%H G. C. Greubel, <a href="/A159506/b159506.txt">Table of n, a(n) for n = 0..422</a>

%F From _G. C. Greubel_, Jun 11 2018: (Start)

%F a(n) = 13^n * Hermite(n,12/13).

%F E.g.f.: exp(24*x-169*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(24/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

%t Numerator[Table[HermiteH[n,12/13],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 14 2011 *)

%o (PARI) a(n)=numerator(polhermite(n,12/13)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(24/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 11 2018

%Y Cf. A159280, A159488.

%K sign,frac

%O 0,2

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