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Numerator of Hermite(n, 11/12).
1

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

%S 1,11,49,-1045,-22079,58091,8587441,69366539,-3565038335,-79170548149,

%T 1439268811441,72834751593131,-338718631136831,-66655130318970325,

%U -416165794764599759,62610547619111490251,1138175082155994132481,-59607424953500501311861

%N Numerator of Hermite(n, 11/12).

%H G. C. Greubel, <a href="/A159486/b159486.txt">Table of n, a(n) for n = 0..450</a>

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

%F a(n) = 6^n * Hermite(n,11/12).

%F E.g.f.: exp(11*x-36*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(11/6)^(n-2*k)/(k!*(n-2*k)!)). (End)

%t Numerator[Table[HermiteH[n,11/12],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 13 2011 *)

%o (PARI) a(n)=numerator(polhermite(n,11/12)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(11/6)^(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.

%K sign,frac

%O 0,2

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