A160197 - OEIS

%I #15 Sep 08 2022 08:45:44

%S 1,15,-167,-14265,-17583,22103775,366019305,-46497789225,

%T -1701823811295,120289709840175,7808380053851385,-354409961765715225,

%U -38985884218692900495,1082356196865530910975,214907408931441984587145,-2716359674426403870623625

%N Numerator of Hermite(n, 15/28).

%H G. C. Greubel, <a href="/A160197/b160197.txt">Table of n, a(n) for n = 0..417</a>

%F From _G. C. Greubel_, Sep 25 2018: (Start)

%F a(n) = 14^n * Hermite(n, 15/28).

%F E.g.f.: exp(15*x - 196*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(15/14)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 15/14, -167/196, -14265/2744, -17583/38416, ...

%t Table[14^n*HermiteH[n, 15/28], {n, 0, 30}] (* _G. C. Greubel_, Sep 25 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 15/28)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(15*x - 196*x^2))) \\ _G. C. Greubel_, Sep 25 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(15/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 25 2018

%Y Cf. A001023 (denominators).

%K sign,frac

%O 0,2

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