|
%I #15 Sep 08 2022 08:45:45
%S 1,38,-478,-164236,-3484820,1130223208,76437602104,-10129105154704,
%T -1413297494585968,102039816064461920,28324733071797627424,
%U -884865408030648260288,-632466392109110072889152,-3625187129327311294505344,15665048162323786452017148800
%N Numerator of Hermite(n, 19/31).
%H G. C. Greubel, <a href="/A160317/b160317.txt">Table of n, a(n) for n = 0..368</a>
%F From _G. C. Greubel_, Oct 04 2018: (Start)
%F a(n) = 31^n * Hermite(n, 19/31).
%F a(n+2) = 38*a(n+1) - 1922*(n+1)*a(n)
%F E.g.f.: exp(38*x - 961*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(38/31)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 38/31, -478/961, -164236/29791, -3484820/923521, ...
%t Numerator[HermiteH[Range[0,20],19/31]] (* _Harvey P. Dale_, Dec 26 2017 *)
%t Table[31^n*HermiteH[n, 19/31], {n, 0, 30}] (* _G. C. Greubel_, Oct 04 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 19/31)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(38*x - 961*x^2))) \\ _G. C. Greubel_, Oct 04 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(38/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Oct 04 2018
%Y Cf. A009975 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
| 