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 A160152 Numerator of Hermite(n, 25/27). 1

%I

%S 1,50,1042,-93700,-9242708,84323000,71595491320,2842116962000,

%T -588597736311920,-62580339060364000,4594562542866814240,

%U 1142149470643447832000,-16580120530325575181120,-20812053164894042027728000,-726343053712911149403451520

%N Numerator of Hermite(n, 25/27).

%H G. C. Greubel, <a href="/A160152/b160152.txt">Table of n, a(n) for n = 0..376</a>

%F From _G. C. Greubel_, Sep 24 2018: (Start)

%F a(n) = 27^n * Hermite(n, 25/27).

%F E.g.f.: exp(50*x - 729*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(50/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 50/27, 1042/729, -93700/19683, -9242708/531441, ...

%t Numerator[HermiteH[Range[0,20],25/27]] (* _Harvey P. Dale_, Nov 15 2014 *)

%t Table[27^n*HermiteH[n, 25/27], {n, 0, 30}] (* _G. C. Greubel_, Sep 24 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 25/27)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(50*x - 729*x^2))) \\ _G. C. Greubel_, Sep 24 2018

%o (MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(50/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 24 2018

%Y Cf. A009971 (denominators).

%K sign,frac

%O 0,2

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

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Last modified January 27 22:10 EST 2022. Contains 350654 sequences. (Running on oeis4.)