A160305 - OEIS

%I #20 Sep 08 2022 08:45:45

%S 1,14,-1726,-77980,8860396,723555784,-75018624584,-9394306045264,

%T 877780290519440,156735773819251424,-12989542631935753184,

%U -3194315169653112913856,229904497949242113022144,76892348044168785827484800,-4667900913141400434386502784

%N Numerator of Hermite(n, 7/31).

%H G. C. Greubel, <a href="/A160305/b160305.txt">Table of n, a(n) for n = 0..368</a>

%F a(n+2) = 14*a(n+1) - 1922*(n+1)*a(n). - _Bruno Berselli_, Mar 28 2018

%F From _G. C. Greubel_, Oct 04 2018: (Start)

%F a(n) = 31^n * Hermite(n, 7/31).

%F E.g.f.: exp(14*x - 961*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(14/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 14/31, -1726/961, -77980/29791, 8860396/923521, ...

%t Numerator[HermiteH[Range[0, 20], 7/31]] (* _Harvey P. Dale_, Apr 23 2016 *)

%t Table[31^n*HermiteH[n, 7/31], {n, 0, 30}] (* _G. C. Greubel_, Oct 04 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 7/31)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(14*x - 961*x^2))) \\ _G. C. Greubel_, Oct 04 2018

%o (Maxima) makelist(num(hermite(n, 7/31)), n, 0, 20); /* _Bruno Berselli_, Mar 28 2018 */

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(14/31)^(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