A159904 - OEIS

%I #17 Sep 08 2022 08:45:44

%S 1,34,98,-68612,-2643860,200474744,20802160696,-565340211248,

%T -173282369297008,-1106561008095200,1612371646170873376,

%U 66528051435456910784,-16502827469331089383232,-1405736274981817978343552,179184855663797992113292160,26914050797599819627076625664

%N Numerator of Hermite(n, 17/23).

%H G. C. Greubel, <a href="/A159904/b159904.txt">Table of n, a(n) for n = 0..385</a>

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

%F a(n) = 23^n * Hermite(n, 17/23).

%F E.g.f.: exp(34*x - 529*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(34/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 34/23, 98/529, -68612/12167, -2643860/279841, ...

%t HermiteH[Range[0,20],17/23]//Numerator (* _Harvey P. Dale_, Apr 08 2018 *)

%t Table[23^n*HermiteH[n, 17/23], {n,0,30}] (* _G. C. Greubel_, Jul 16 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 17/23)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(34*x - 529*x^2))) \\ _G. C. Greubel_, Jul 16 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(34/23)^(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. A009967 (denominators).

%K sign,frac

%O 0,2

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