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 A159485 Numerator of Hermite(n, 7/12). 1

%I

%S 1,7,-23,-1169,-3215,314167,3356569,-112224161,-2477279903,

%T 47300157415,1936378479049,-20501463985457,-1677122003305007,

%U 5973410860299799,1611600071115585145,5260002350626898623,-1703708060350443666239,-17985479130375292877369

%N Numerator of Hermite(n, 7/12).

%H G. C. Greubel, <a href="/A159485/b159485.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,7/12).

%F E.g.f.: exp(7*x-36*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(7/6)^(n-2*k)/(k!*(n-2*k)!)). (End)

%t Numerator[Table[HermiteH[n,7/12],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 13 2011 *)

%o (PARI) a(n)=numerator(polhermite(n,7/12)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(7/6)^(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

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Last modified June 14 08:09 EDT 2021. Contains 345018 sequences. (Running on oeis4.)