A160221 - OEIS

%I #11 Sep 08 2022 08:45:45

%S 1,23,137,-14881,-503375,11755783,1256998009,1261352591,

%T -3420191427103,-82620004548745,10166175250198249,557692448585640127,

%U -31009621361385126767,-3336606569458709073049,81283079360068297324505,20180807678470966231356527,-13785930032369364946889279

%N Numerator of Hermite(n, 23/28).

%H G. C. Greubel, <a href="/A160221/b160221.txt">Table of n, a(n) for n = 0..417</a>

%F From _G. C. Greubel_, Sep 26 2018: (Start)

%F a(n) = 14^n * Hermite(n, 23/28).

%F E.g.f.: exp(23*x - 196*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(23/14)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 23/14, 137/196, -14881/2744, -503375/38416

%t Table[14^n*HermiteH[n, 23/28], {n, 0, 30}] (* _G. C. Greubel_, Sep 26 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 23/28)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(23*x - 196*x^2))) \\ _G. C. Greubel_, Sep 26 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(23/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 26 2018

%Y Cf. A001023 (denominators).

%K sign,frac

%O 0,2

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