A160062 - OEIS

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

%S 1,34,-94,-88196,-2646164,351010424,28472879416,-1664500279856,

%T -305730704405104,6250158848786464,3651975825416159776,

%U 46040192454318632384,-48649301056025363418944,-2344679122719641842004096,710832051987944332929700736,65200174415183839554681505024

%N Numerator of Hermite(n, 17/25).

%H G. C. Greubel, <a href="/A160062/b160062.txt">Table of n, a(n) for n = 0..380</a>

%F From _G. C. Greubel_, Sep 23 2018: (Start)

%F a(n) = 25^n * Hermite(n, 17/25).

%F E.g.f.: exp(34*x - 625*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(34/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 34/25, -94/625, -88196/15625, -2646164/390625, ...

%t Numerator[HermiteH[Range[0,20],17/25]] (* _Harvey P. Dale_, Feb 04 2015 *)

%t Table[25^n*HermiteH[n, 17/25], {n, 0, 30}] (* _G. C. Greubel_, Sep 23 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 17/25)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(34*x - 625*x^2))) \\ _G. C. Greubel_, Sep 23 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(34/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 23 2018

%Y Cf. A009969 (denominators).

%K sign,frac

%O 0,2

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