|
%I #13 Sep 08 2022 08:45:44
%S 1,32,-226,-87232,-1943924,373954432,24116066824,-2032944101632,
%T -276069795962224,11495207545528832,3473631846031942624,
%U -32533875246088236032,-48803521890814034633024,-1073704571814725567776768,758698684427656844617783424,43068187908442716463862509568
%N Numerator of Hermite(n, 16/25).
%H G. C. Greubel, <a href="/A160061/b160061.txt">Table of n, a(n) for n = 0..380</a>
%F From _G. C. Greubel_, Sep 23 2018: (Start)
%F a(n) = 25^n * Hermite(n, 16/25).
%F E.g.f.: exp(32*x - 625*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(32/25)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 32/25, -226/625, -87232/15625, -1943924/390625, ...
%t Numerator[Table[HermiteH[n, 16/25], {n, 0, 50}]] (* _G. C. Greubel_, Sep 23 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 16/25)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(32*x - 625*x^2))) \\ _G. C. Greubel_, Sep 23 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(32/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 23 2018
%Y Cf. A009969 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
| 