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Numerator of Hermite(n, 1/16).
8

%I #11 Sep 08 2022 08:45:43

%S 1,1,-127,-383,48385,244481,-30721919,-218483327,27308356097,

%T 251035282945,-31208190940799,-352533353110399,43588599491534593,

%U 585079829869107457,-71946349724044455295,-1120409404849485018239,137016582065315869148161

%N Numerator of Hermite(n, 1/16).

%H G. C. Greubel, <a href="/A159521/b159521.txt">Table of n, a(n) for n = 0..450</a>

%F From _G. C. Greubel_, Jun 09 2018: (Start)

%F a(n) = 8^n * Hermite(n,1/16).

%F E.g.f.: exp(2*x-64*x^2).

%F a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/8)^(n-2k)/(k!*(n-2k)!). (End)

%t Numerator[Table[HermiteH[n,1/16],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 28 2011 *)

%o (PARI) a(n)=numerator(polhermite(n,1/16)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(1/8)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 09 2018

%Y Cf. A159513.

%K sign,frac

%O 0,3

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