A159859 - OEIS

%I #12 Sep 08 2022 08:45:44

%S 1,4,-1042,-12632,3256780,66485744,-16962423224,-489901195808,

%T 123664101613712,4641180127773760,-1158964855054670624,

%U -53739545172065063296,13273074802437996468928,735369564714290029481728,-179616392573875043315708800,-11610759562843564089946190336

%N Numerator of Hermite(n, 2/23).

%H G. C. Greubel, <a href="/A159859/b159859.txt">Table of n, a(n) for n = 0..385</a>

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

%F a(n) = 23^n * Hermite(n, 2/23).

%F E.g.f.: exp(4*x-529*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

%t Numerator[Table[HermiteH[n, 2/23], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 22 2011 *)

%t Table[23^n*HermiteH[n, 2/23], {n,0,30}] (* _G. C. Greubel_, Jul 09 2018 *)

%o (PARI) a(n)=numerator(polhermite(n,2/23)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(4/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 09 2018

%Y Cf. A159858.

%K sign,frac

%O 0,2

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