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Numerator of Hermite(n, 11/16).
1

%I #17 Sep 08 2022 08:45:43

%S 1,11,-7,-2893,-29135,1160731,31414441,-545882557,-34152047263,

%T 183311218475,41359581850201,220317040704211,-55810803797336687,

%U -952325816292371653,82393593539552158985,2612897391731003751011,-129453828286899103990079

%N Numerator of Hermite(n, 11/16).

%H G. C. Greubel, <a href="/A159526/b159526.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, 11/16).

%F E.g.f.: exp(11*x-64*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(11/8)^(n-2*k)/(k!*(n-2*k)!)). (End)

%t Numerator[Table[HermiteH[n,11/16],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 29 2011 *)

%o (PARI) a(n)=numerator(polhermite(n,11/16)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(11/8)^(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. A159521.

%K sign,frac

%O 0,2

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