A159997 - OEIS

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

%S 1,19,73,-9557,-244655,6361219,473166361,-2002025573,-991941869663,

%T -14234228603405,2300662982701801,84707175049140619,

%U -5679064003265633807,-400650213031877021597,13650061580620869563065,1874772828976324672777339,-23347582277731987729671359

%N Numerator of Hermite(n, 19/24).

%H G. C. Greubel, <a href="/A159997/b159997.txt">Table of n, a(n) for n = 0..428</a>

%F From _G. C. Greubel_, Jul 16 2018: (Start)

%F a(n) = 12^n * Hermite(n, 19/24).

%F E.g.f.: exp(19*x - 144*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(19/12)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 19/12, 73/144, -9557/1728, -244655/20736, ...

%t Numerator[HermiteH[Range[0,20],19/24]] (* _Harvey P. Dale_, Jun 12 2016 *)

%t Table[12^n*HermiteH[n, 19/12], {n, 0, 30}] (* _G. C. Greubel_, Jul 16 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 19/24)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(19*x - 144*x^2))) \\ _G. C. Greubel_, Jul 16 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(19/12)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 16 2018

%Y Cf. A001021 (denominators).

%K sign,frac

%O 0,2

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